provide a sense of the absurdities this can lead to, assume that you are picking

between two mutually exclusive projects with the cash flows shown in Figure 5.2:

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Figure 5.2: Using Payback for Mutually Exclusive Projects

Project A

$ 400 $ 300 $ 10,000

Cash Flow $ 300

Investment $ 1000

Payback = 3 years

Project B

$ 500 $ 100 $ 100

Cash Flow $ 500

Investment $ 1000

Payback = 2 years

On the basis of the payback alone, project B is preferable to project A, since it has a

shorter payback period. Most decision makers would pick project A as the better

project, however, because of the high cash flows that result after the initial investment

is paid back.

The payback rule is designed to cover the conventional project that involves a large

•

up-front investment followed by positive operating cash flows. It breaks down,

however, when the investment is spread over time or when there is no initial

investment.

The payback rule uses nominal cash flows and counts cash flows in the early years

•

the same as cash flows in the later years. Since money has time value, however,

recouping the nominal initial investment does not make the business whole again,

since that amount could have been invested elsewhere and earned a significant return.

Discounted Cash Flow Measures

Investment decision rules based on discounted cash flows not only replace

accounting income with cash flows, but explicitly factor in the time value of money. The

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two most widely used discounted cash flows rules are net present value and the internal

rate of return.

Net Present Value (NPV)

The net present value of a project is the sum of the present values of each of the

cash flows ““ positive as well as negative ““ that occurs over the life of the project. The

general formulation of the NPV rule is as follows

t=N

CFt

! (1 + r)t - Initial Investment

NPV of Project =

t=1

where

CFt = Cash flow in period t Net Present Value (NPV): The net present value of

r = Discount rate a project is the sum of the present values of the

expected cash flows on the project, net of the initial

N = Life of the project

investment.

Thus, the net present value of a project with

the cash flows depicted in Figure 5.3 and a

discount rate of 12% can be written as:

Once the net present value is computed, the decision rule is extremely simple since the

hurdle rate is already factored in the present value.

Decision Rule for NPV for Independent Projects

If the NPV > 0 -> Accept the project

If the NPV < 0 -> Reject the project

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Note that a net present value that is greater than zero implies that the project makes a

return greater than the hurdle rate. The following examples illustrate the two approaches.

This spreadsheet allows you to estimate the NPV from cash flows to the firm on a

project

5.9. ˜: The Significance of a positive Net Present Value

Assume that you have analyzed a $100 million project, using a cost of capital of 15%,

and come up with a net present value of $ 1 million. The manager who has to decide on

the project argues that this is too small of a NPV for a project of this size, and that this

indicates a “poor” project. Is this true?

a. Yes. The NPV is only 1% of the initial investment

b. No. A positive NPV indicates a good project

Explain your answer.

Illustration 5.11: NPV From The Firm™s Standpoint - Bookscape On-line

Table 5.13 calculates the present value of the cash flows to Bookscape, as a firm,

from the proposed on-line book ordering service, using the cost of capital of 22.76% as

the discount rate on the cash flows. (The cash flows are estimated in illustration 5.4 and

the cost of capital is estimated in illustration 5.2)

Table 5.13: FCFF on Bookscape On-line

Year Annual Cashflow PV of Cashflow

0 ($1,150,000) $ (1,150,000)

1 $ 340,000 $ 276,969

2 $ 415,000 $ 275,392

3 $ 446,500 $ 241,366

4 $ 720,730 $ 317,380

NPV $ (38,893)

This project has a net present value of -$38,893, suggesting that it is a project that should

not be accepted, based on the projected cash flows and the cost of capital of 22.76%.

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Illustration 5.12: NPV From The Firm™s Standpoint - Disney™s Theme Park in Bangkok

In estimating the cash flows to discount for Disney™s theme park in Thailand, the

first point to note when computing the net present value of the proposed theme park in

Thailand is the fact that it has a life far longer than the ten years shown in exhibit 5.2. To

bring in the cash flows that occur after year 10, when cash flows start growing at 2%, the

inflation rate forever, we draw on a present value formula for a growing perpetuity (See

appendix 1):

Present Value of Cash Flows after year 10 = FCFF11/(WACC - g)

= $ 663 million/(.1066-.02)

= $7,810 million

The cost of capital of 10.66% is the cost of capital for Bangkok theme park that we

estimated in illustration 5.2. This present value is called the terminal value and occurs at

the end of year 10.

Table 5.14 presents the net present value of the proposed theme parks in Thailand

are estimated using the cash flows in nominal dollars, from exhibit 5.2, and Disney™s cost

of capital, in dollar terms, of 10.66%.

Table 5.14: Net Present Value of Disney Bangkok Theme Park

Year Annual Cashflow Terminal Value Present Value

0 -$2,000 -$2,000

1 -$1,000 -$904

2 -$880 -$719

3 -$289 -$213

4 $324 $216

5 $443 $267

6 $486 $265

7 $517 $254

8 $571 $254

9 $631 $254

10 $663 $7,810 $3,076

$749

The net present value of this project is positive. This suggests that it is a good project that

will earn surplus value for Disney.

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NPV and Currency Choices

When analyzing a project, the cashflows and discount rates can often be estimated in

one of several currencies. For a project like the Disney theme park, the obvious choices

are the project™s local currency (Thai Baht) and the company™s domicile currency (U.S.

dollars) but we can in fact use any currency to evaluate the project. When switching from

one currency to another, we have to go through the following steps:

1. Estimate the expected exchange rate for each period of the analysis: For some

currencies (Euro, Yen or British pound), we can estimates of expected exchange

rates from the financial markets in the form of forward rates. For other currencies,

we weill have to estimate the exchange rate and the safest way to do so is to use

the expected inflation rates in the two currencies in question. For instance, we can

estimate the expected Baht/$ exchange rate in n years:

n

"(1 + Expected InflationThailand ) %

Expected Rate (Bt/$) = Bt/$ (Today) * $ '

# (1 + Expected InflationUS ) &

We are assuming that purchasing power ultimately drives exchange rates “ this is

called purchasing power parity.

!

2. Convert the expected cashflows from one currency to another in future periods,

using these exchange rates: Multiplying the expected cashflows in one currency

to another will accomplish this.

3. Convert the discount rate from one currency to another: We cannot discount

cashflows in one currency using discount rates estimated in another. To convert a

discount rate from one currency to another, we will again use expected inflation

rates in the two currencies. A dollar cost of capital can be converted into a Thai

Baht cost of capital as follows:

(1+ Exp InflationThailand )

Cost of Capital(Bt) = (1 + Cost of Capital ($)) * "1

(1+ Exp InflationUS )

a. Compute the net present value by discounting the converted cashflows (from step

2) at the converted discount rate (from step 3): The net present value should be

!

identical in both currencies but only because the expected inflation rate was used

to estimate the exchange rates. If the forecasted exchange rates diverge from

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purchasing power parity, we can get different net present values but our currency

views are then contaminating our project analysis.

Illustration 5.13: NPV In Thai Baht - Disney™s Theme Park in Bangkok

In illustration 5.12, we computed the net present value for the Disney Theme park

in dollar terms to be $2,317 million. The entire analysis could have been done in Thai

Baht terms. To do this, the cash flows would have to be converted from dollars to Thai

Baht and the discount rate would then have been a Thai Baht discount rate. To estimate

the expected exchange rate, we will assume that the expected inflation rate to be 10% in

Thailand and 2% in the United States and the current exchange rate is 42.09 Bt per dollar,

the projected exchange rate in one year will be:

Expected Exchange Rate in year 1 = 42.09 Bt * (1.10/1.02) = 45.39 Bt/$

Similar analysis will yield exchange rates for each of the next 10 years.

The dollar cost of capital of 10.35%, estimated in illustration 5.1, is converted to a

Baht cost of capital using the expected inflation rates:

(1+ Exp InflationThailand )

Cost of Capital (Bt) = (1 + Cost of Capital ($)) * "1

(1+ Exp InflationUS )

= (1.1066) (1.10/1.02) “ 1 = 19.34%

Table 5.15 summarizes exchange rates, cash flows and the present value for the proposed

!

Disney theme parks, with the analysis done entirely in Thai Baht.

Table 5.15: Expected Cashflows from Disney Theme Park in Thai Bt

Year Cashflow ($) Bt/$ Cashflow (Bt) Present Value

0 -2000 42.09 -84180 -84180

1 -1000 45.39 -45391 -38034

2 -880 48.95 -43075 -30243

3 -289 52.79 -15262 -8979

4 324 56.93 18420 9080

5 443 61.40 27172 11223

6 486 66.21 32187 11140

7 517 71.40 36920 10707

8 571 77.01 43979 10687

9 631 83.04 52412 10671

10 8474 89.56 758886 129470

NPV of Disney Theme Park = 31,542

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Note that the net present value of 31,542 million Bt is exactly equal to the dollar net

present value computed in illustration 5.12, converted at the current exchange rate of

42.09 Bt per dollar.

NPV in dollars = NPV in Bt/ Current exchange rate = 31,542/42.09 = $749 million

Terminal Value, Salvage Value and Net Present Value

When estimating cashflows for an individual project, practicality constrains us to