- Select the investment plan
The firm should adopt plan A because it has the lower payback period.
Related Calculations: The investment rate is 6.0 percent for plan A and 10.0
percent for plan B. However, since the income under plan B is largely deferred, use of the
payback period as a criterion in investment appraisal places plan B at a disadvantage.
PAYBACKPERIOD TO YIELD
A GIVEN INVESTMENT RATE
An asset has a first cost of $40,000 and maximum life of 10 years. Its resale value will be
$3500 at the end of the first year, and then it will diminish by $500 per year, becoming
zero at the end of the eighth year. The end-of-year income that accrues from use of this
asset will be $12,000 for the first 2 years, $8000 for the next 3 years, $6000 for the next 3
years, and $2000 for the last 2 years. Determine how long this asset must be held to se-
cure a 10 percent return on the investment.
Calculation Procedure:
- Establish the criterion for finding the life of the asset
As the preceding calculation procedure showed, a firm that considers solely how long it
takes an investment to restore the sum invested is apt to undertake investments of rela-
tively low yield. A more logical approach is to consider how long it takes an investment
to restore the sum invested and yield a certain minimum rate of return.
Let TV= life of asset, years; / and /' = required investment rate and true investment rate,
respectively; Fexp, and Finc = value of expenditures and value of income, respectively,
where all sums of money are evaluated at a specific date and by using / as the interest rate.
If Fexp = Finc, then /' = /. Thus, the problem is to find the value of Af at which this equality
of expenditures and income becomes a fact. - Perform the calculations
Evaluate all sums of money at the date of purchase, using an interest rate of 10 percent.
Set N= 1. Then Kexp, = $40,000 - $3500(SPPW, n = 1) = $40,000 - $3500(0.90909) =
$36,818. Also, = $12,000(0.90909) = $10,909. Since Fexp > Finc, i' < 10 percent.
Now set N = 2. Then Fexp - $40,000 - $3000(SPPW, n = 2) = $40,000 -
$3000(0.82645) = $37,521. Applying the previous result and adding the income at the
end of the second year, we find Finc = $10,909 + $12,000(0.82645) = $20,826. Thus, /' <
10 percent.
Set N= 3. Then Fexp = $40,000 - $2500(0.75131) = $38,122. Also, Finc = $20,826 +
$8000(0.75131) = $26,836.
Continue these calculations to obtain the results in Table 15. This table shows that i' <
10 percent when N= 5 and i' > 10 percent when N= 6. Thus, the asset must be held 6
years to secure a 10 percent rate of return.
BENEFIT-COST A NALYSIS
A proposed flood-control dam is expected to have an initial cost of $5,000,000 and to re-
quire annual maintenance of $24,00.0. It will also require major repairs and reconstruction