Question

Atlas Corp. is considering two mutually exclusive projects. Both require an initial investment of $10,000 at t = 0. Project S has an expected life of 2 years with after-tax cash inflows of $6,000 and $8,000 at the end of Years 1 and 2, respectively. Project L has an expected life of 4 years with after-tax cash inflows of $4,373 at the end of each of the next 4 years. Each project has a WACC of 9.25%, and Project S can be repeated with no changes in its cash flows. The controller prefers Project S, but the CFO prefers Project L. How much value will the firm gain or lose if Project L is selected over Project S, i.e., what is the value of NPVL - NPVS?a. $56.50b. $62.15c. $68.37d. $75.21e. $82.73

Answer 1

Answer:

A) $56.5

Explanation:

Data:

Project S

Initial cost $10,000

Y1 CF = $6,000

y2 CF = $8,000

Project L

Initial Investment = $10,000

Y1-Y4 CF = $4,373

Solution:

For Project S

We shall prolong the project to four years so it can be easily compared to project L

Following shall be the cashflow stream:

Y0=-$10,000  Y1=$6,000  Y2=-$2,000($8,000 CF - $10,000 outlay for prolonging the project second time)  Y3=$6,000  Y4=$8,000

Now to discount the cashflow

$NPV=-10000/(1+0.0925)^0+6000/(1+0.0925)^1-2000/(1+0.0925)^2+6000/(1+0.0925)^3+8000/(1+0.0925)^4$

$NPV=4033.40$

For Project L

In order to calculate present value of the annuity, following formula will be used:

$PV=PMT(1+(1/(1+r)^n)/r$

NPV = Initial outlay - PV

$4373(1+(1/(1+0.0925)^4)/0.0925=14089.9$

$NPV=-10000+14089.9$

$NPV=4089.9$

Now, we can easily calculate how much value will the firm gain or lose if Project L is selected over Project S

$Value=NPV(L)-NPV(S)$

$Value=4033.40-4089.90$

$Value=56.50$

*all figures are rounded off to two decimal points*