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is the same in Greece, then expected inflation must be (1 + nominal rate)/(1 + real rate) “
1 = 1.085/1.039 “ 1 = .044, or 4.4%.
6 The Swiss franc is at a forward premium (that is, you get fewer francs for $1 in the forward
market). This implies that interest rates in Switzerland are lower than in the United States.
The interest rate in the United States is 6 percent. Interest rate parity states
622 SECTION SIX


1 + rfranc ffranc/$
=
1 + r$ sfranc/$
1.4331
rfranc = 1.06 —
Therefore “ 1 = .022, or 2.2%
1.4865
7 Stellar borrows ¥100 million in 1998. It pays ¥2 million in interest at the end of 1999, when
it also repays the loan. Cash flows in dollars are:
+ 100 million
1998: = +$806,647
123.97
2 million
1999: Interest = = $ 18,601
107.52
100 million
Principal = = 930,059
107.52
Total $948,661

To find the dollar interest rate, solve
806,647 — (1 + r$) = 948,661
948,661
r$ = “ 1 = .176 = 17.6%
806,647
8 According to the expectations theory of exchange rates, the forward rate equals the ex-
pected future spot exchange rate. Therefore, the expected cost of the hedge”the difference
between the forward rate and expected spot rate”is zero!

9 a. The lower interest rate in Narnia than in the United States suggests that forecast inflation
is lower in Narnia. If real interest rates are the same in the two countries, then the dif-
ference in inflation rates is about 5 “ 3 = 2 percent.
b. The lower interest rate (and lower expected inflation rate) in Narnia suggests that in-
vestors are expecting the leo to appreciate against the dollar.
c. Since KW can now expect to change its leo cash flows into more dollars than before, the
project™s NPV is increased. Forecast exchange rates will be as follows:

Year Forecast Exchange Rate
0 Spot exchange rate = L2.00/$
2.00 — (1.03/1.05) = L1.962/$
1
2.00 — (1.03/1.05)2 = L1.925/$
2
2.00 — (1.03/1.05)3 = L1.888/$
3
2.00 — (1.03/1.05)4 = L1.852/$
4
2.00 — (1.03/1.05)5 = L1.817/$
5

The expected dollar cash flows from the project are

Year 0 1 2 3 4 5
Cash flow “7.6 2.0 2.5 3.0 3.5 4.0
(millions 2.00 1.962 1.925 1.888 1.852 1.817
of dollars) = “$3.8 = $1.02 = $1.30 = $1.59 = $1.89 = $2.20

Discounting these dollar cash flows at the 15 percent dollar cost of capital gives
1.02 1.30 1.59 1.89 2.20
NPV = “ 3.8 + + + + +
1.15 1.15 1.15 1.15
2 3 4 1.155
= $1.29 million, or $1,290,000
International Financial Management 623


The project is worth more because the reduced interest rate in Narnia suggests that investors
expect the leo to appreciate in value. Thus the dollar cash flows from the project are higher
than in Section 6.4.




MINICASE
“Jumping jackasses! Not another one!” groaned George Luger.
This was the third memo that he had received that morning from
the CEO of VCR Importers. It read as follows:


From: CEO™s Office
To: Company Treasurer

George,

I have been looking at some of our foreign exchange deals and they don™t seem to make sense.
First, we have been buying yen forward to cover the cost of our imports. You have explained that this insures us against the
risk that the dollar may depreciate over the next year, but it is incredibly expensive insurance. Each dollar buys only 101.3 yen when
we buy forward, compared with the current spot rate of 107.52 yen to the dollar. We could save a fortune by buying yen as and
when we need them rather than buying them forward.
Another possibility has occurred to me. If we are worried that the dollar may depreciate (or do I mean “appreciate”?), why
don™t we buy yen at the low spot rate of ¥107.52 to the dollar and then put them on deposit until we have to pay for the VCRs? That
way we can make sure that we get a good rate for our yen.
I am also worried that we are missing out on some cheap financing. We are paying about 8 percent to borrow dollars for one
year, but Ben Hur was telling me at lunch that we could get a one-year yen loan for about 1.75 percent. I find that a bit surprising,
but if that™s the case, why don™t we repay our dollar loans and borrow yen instead?
Perhaps we could discuss these ideas at next Wednesday™s meeting. I would be interested in your views on the matter.

Jill Edison
Appendix C
PRESENT VALUE TABLES
626




APPENDIX TABLE C.1
FUTURE VALUE OF $1 AFTER t YEARS = (1 + r)t

Interest Rate per Year
Number
APPENDIX C Present Value Tables




of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120 1.130 1.140 1.150
2 1.020 1.040 1.061 1.082 1.102 1.124 1.145 1.166 1.188 1.210 1.232 1.254 1.277 1.300 1.323
3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.368 1.405 1.443 1.482 1.521
4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.518 1.574 1.630 1.689 1.749
5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 1.685 1.762 1.842 1.925 2.011
6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 1.870 1.974 2.082 2.195 2.313
7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.076 2.211 2.353 2.502 2.660
8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.305 2.476 2.658 2.853 3.059
9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 2.558 2.773 3.004 3.252 3.518
10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 2.839 3.106 3.395 3.707 4.046
11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 3.152 3.479 3.836 4.226 4.652
12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 3.498 3.896 4.335 4.818 5.350
13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 3.883 4.363 4.898 5.492 6.153
14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797 4.310 4.887 5.535 6.261 7.076
15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 4.785 5.474 6.254 7.138 8.137
16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 5.311 6.130 7.067 8.137 9.358
17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 5.895 6.866 7.986 9.276 10.76
18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 6.544 7.690 9.024 10.58 12.38
19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 7.263 8.613 10.20 12.06 14.23
20 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727 8.062 9.646 11.52 13.74 16.37
25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.83 13.59 17.00 21.23 26.46 32.92
30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.06 13.27 17.45 22.89 29.96 39.12 50.95 66.21
Interest Rate per Year
Number
of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%
1 1.160 1.170 1.180 1.190 1.200 1.210 1.220 1.230 1.240 1.250 1.260 1.270 1.280 1.290 1.300
2 1.346 1.369 1.392 1.416 1.440 1.464 1.488 1.513 1.538 1.563 1.588 1.613 1.638 1.664 1.690
3 1.561 1.602 1.643 1.685 1.728 1.772 1.816 1.861 1.907 1.953 2.000 2.048 2.097 2.147 2.197
4 1.811 1.874 1.939 2.005 2.074 2.144 2.215 2.289 2.364 2.441 2.520 2.601 2.684 2.769 2.856
5 2.100 2.192 2.288 2.386 2.488 2.594 2.703 2.815 2.932 3.052 3.176 3.304 3.436 3.572 3.713
6 2.436 2.565 2.700 2.840 2.986 3.138 3.297 3.463 3.635 3.815 4.002 4.196 4.398 4.608 4.827
7 2.826 3.001 3.185 3.379 3.583 3.797 4.023 4.259 4.508 4.768 5.042 5.329 5.629 5.945 6.275
8 3.278 3.511 3.759 4.021 4.300 4.595 4.908 5.239 5.590 5.960 6.353 6.768 7.206 7.669 8.157
9 3.803 4.108 4.435 4.785 5.160 5.560 5.987 6.444 6.931 7.451 8.005 8.595 9.223 9.893 10.60
10 4.411 4.807 5.234 5.695 6.192 6.728 7.305 7.926 8.594 9.313 10.09 10.92 11.81 12.76 13.79
11 5.117 5.624 6.176 6.777 7.430 8.140 8.912 9.749 10.66 11.64 12.71 13.86 15.11 16.46 17.92
12 5.936 6.580 7.288 8.064 8.916 9.850 10.87 11.99 13.21 14.55 16.01 17.61 19.34 21.24 23.30
13 6.886 7.699 8.599 9.596 10.70 11.92 13.26 14.75 16.39 18.19 20.18 22.36 24.76 27.39 30.29
14 7.988 9.007 10.15 11.42 12.84 14.42 16.18 18.14 20.32 22.74 25.42 28.40 31.69 35.34 39.37
15 9.266 10.54 11.97 13.59 15.41 17.45 19.74 22.31 25.20 28.42 32.03 36.06 40.56 45.59 51.19
16 10.75 12.33 14.13 16.17 18.49 21.11 24.09 27.45 31.24 35.53 40.36 45.80 51.92 58.81 66.54
17 12.47 14.43 16.67 19.24 22.19 25.55 29.38 33.76 38.74 44.41 50.85 58.17 66.46 75.86 86.50
18 14.46 16.88 19.67 22.90 26.62 30.91 35.85 41.52 48.04 55.51 64.07 73.87 85.07 97.86 112.5
19 16.78 19.75 23.21 27.25 31.95 37.40 43.74 51.07 59.57 69.39 80.73 93.81 108.9 126.2 146.2
20 19.46 23.11 27.39 32.43 38.34 45.26 53.36 62.82 73.86 86.74 101.7 119.1 139.4 162.9 190.0
25 40.87 50.66 62.67 77.39 95.40 117.4 144.2 176.9 216.5 264.7 323.0 393.6 478.9 581.8 705.6
30 85.85 111.1 143.4 184.7 237.4 304.5 389.8 497.9 634.8 807.8 1026 1301 1646 2078 2620

e.g., if the interest rate is 10 percent per year, the investment of $1 today will be worth $1.611 at year 5.
APPENDIX C Present Value Tables
627
628




APPENDIX TABLE C.2
DISCOUNT FACTORS: PRESENT VALUE OF $1 TO BE RECEIVED AFTER t YEARS = 1/(1 + r)t

Interest Rate per Year
Number
APPENDIX C Present Value Tables




of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
1 .990 .980 .971 .962 .952 .943 .935 .926 .917 .909 .901 .893 .885 .877 .870
2 .980 .961 .943 .925 .907 .890 .873 .857 .842 .826 .812 .797 .783 .769 .756
3 .971 .942 .915 .889 .864 .840 .816 .794 .772 .751 .731 .712 .693 .675 .658
4 .961 .924 .888 .855 .823 .792 .763 .735 .708 .683 .659 .636 .613 .592 .572
5 .951 .906 .863 .822 .784 .747 .713 .681 .650 .621 .593 .567 .543 .519 .497
6 .942 .888 .837 .790 .746 .705 .666 .630 .596 .564 .535 .507 .480 .456 .432
7 .933 .871 .813 .760 .711 .665 .623 .583 .547 .513 .482 .452 .425 .400 .376
8 .923 .853 .789 .731 .677 .627 .582 .540 .502 .467 .434 .404 .376 .351 .327
9 .914 .837 .766 .703 .645 .592 .544 .500 .460 .424 .391 .361 .333 .308 .284
10 .905 .820 .744 .676 .614 .558 .508 .463 .422 .386 .352 .322 .295 .270 .247
11 .896 .804 .722 .650 .585 .527 .475 .429 .388 .350 .317 .287 .261 .237 .215
12 .887 .788 .701 .625 .557 .497 .444 .397 .356 .319 .286 .257 .231 .208 .187
13 .879 .773 .681 .601 .530 .469 .415 .368 .326 .290 .258 .229 .204 .182 .163
14 .870 .758 .661 .577 .505 .442 .388 .340 .299 .263 .232 .205 .181 .160 .141
15 .861 .743 .642 .555 .481 .417 .362 .315 .275 .239 .209 .183 .160 .140 .123
16 .853 .728 .623 .534 .458 .394 .339 .292 .252 .218 .188 .163 .141 .123 .107
17 .844 .714 .605 .513 .436 .371 .317 .270 .231 .198 .170 .146 .125 .108 .093
18 .836 .700 .587 .494 .416 .350 .296 .250 .212 .180 .153 .130 .111 .095 .081
19 .828 .686 .570 .475 .396 .331 .277 .232 .194 .164 .138 .116 .098 .083 .070
20 .820 .673 .554 .456 .377 .312 .258 .215 .178 .149 .124 .104 .087 .073 .061
25 .780 .610 .478 .375 .295 .233 .184 .146 .116 .092 .074 .059 .047 .038 .030
30 .742 .552 .412 .308 .231 .174 .131 .099 .075 .057 .044 .033 .026 .020 .015
Interest Rate per Year
Number
of Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%
1 .862 .855 .847 .840 .833 .826 .820 .813 .806 .800 .794 .787 .781 .775 .769
2 .743 .731 .718 .706 .694 .683 .672 .661 .650 .640 .630 .620 .610 .601 .592
3 .641 .624 .609 .593 .579 .564 .551 .537 .524 .512 .500 .488 .477 .466 .455
4 .552 .534 .516 .499 .482 .467 .451 .437 .423 .410 .397 .384 .373 .361 .350
5 .476 .456 .437 .419 .402 .386 .370 .355 .341 .328 .315 .303 .291 .280 .269
6 .410 .390 .370 .352 .335 .319 .303 .289 .275 .262 .250 .238 .227 .217 .207
7 .354 .333 .314 .296 .279 .263 .249 .235 .222 .210 .198 .188 .178 .168 .159
8 .305 .285 .266 .249 .233 .218 .204 .191 .179 .168 .157 .148 .139 .130 .123
9 .263 .243 .225 .209 .194 .180 .167 .155 .144 .134 .125 .116 .108 .101 .094
10 .227 .208 .191 .176 .162 .149 .137 .126 .116 .107 .099 .092 .085 .078 .073
11 .195 .178 .162 .148 .135 .123 .112 .103 .094 .086 .079 .072 .066 .061 .056
12 .168 .152 .137 .124 .112 .102 .092 .083 .076 .069 .062 .057 .052 .047 .043
13 .145 .130 .116 .104 .093 .084 .075 .068 .061 .055 .050 .045 .040 .037 .033
14 .125 .111 .099 .088 .078 .069 .062 .055 .049 .044 .039 .035 .032 .028 .025
15 .108 .095 .084 .074 .065 .057 .051 .045 .040 .035 .031 .028 .025 .022 .020
16 .093 .081 .071 .062 .054 .047 .042 .036 .032 .028 .025 .022 .019 .017 .015
17 .080 .069 .060 .052 .045 .039 .034 .030 .026 .023 .020 .017 .015 .013 .012
18 .069 .059 .051 .044 .038 .032 .028 .024 .021 .018 .016 .014 .012 .010 .009
19 .060 .051 .043 .037 .031 .027 .023 .020 .017 .014 .012 .011 .009 .008 .007
20 .051 .043 .037 .031 .026 .022 .019 .016 .014 .012 .010 .008 .007 .006 .005
25 .024 .020 .016 .013 .010 .009 .007 .006 .005 .004 .003 .003 .002 .002 .001
30 .012 .009 .007 .005 .004 .003 .003 .002 .002 .001 .001 .001 .001 .000 .000

e.g., if the interest rate is 10 percent per year, the present value of $1 received at year 5 is $.621.
APPENDIX C Present Value Tables
629
630




APPENDIX TABLE C.3
ANNUITY TABLE: PRESENT VALUE OF $1 PER YEAR FOR EACH OF t YEARS = 1/r “ 1/[r(1 + r)t ]

Interest Rate per Year
Number
APPENDIX C Present Value Tables




of Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
1 .990 .980 .971 .962 .952 .943 .935 .926 .917 .909 .901 .893 .885 .877 .870
2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 1.668 1.647 1.626
3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 2.361 2.322 2.283
4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.974 2.914 2.855
5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.517 3.433 3.352
6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 3.998 3.889 3.784
7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 4.423 4.288 4.160
8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 4.799 4.639 4.487
9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 5.132 4.946 4.772
10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.426 5.216 5.019
11 10.37 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 5.687 5.453 5.234
12 11.26 10.58 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 5.918 5.660 5.421

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