Question

The Sampson Company is considering a project that requires an initial outlay of $75,000 and produces cash inflows of $20,806 each year for five years. Sampson's cost of capital is 8%.

1. Calculate the project's payback period by making a single division rather than accumulating cash inflows. Round the answer to two decimal places.
   year(s)
   
2. Calculate the project's IRR, recognizing the fact that the cash inflows are an annuity. Round PVFA values in intermediate calculations to four decimal places. Round the answer to the nearest whole percentage.
   %
   
   Is the project acceptable?
   No
   
   Did your calculation in this part result in any number(s) that were also calculated in part (a)? What is it about this problem that creates this similarity? Will this always happen in such cases?
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
3. What is the project's NPV? Do not round intermediate calculations. Round PVFA values in intermediate calculations to four decimal places. Round the answer to two decimal places.
   $
   
   Is the project acceptable according to NPV rules?
   Yes

Answer 1

Answer (a):

As annual cash flows are constant, for payback period we can use the formula:

Payback period = Initial Investment / Annual cash flow = 75000 / 20806 = 3.6047 Years

Payback period = 3.60 Years

Answer (b):

At discount rate = IRR, NPV will be equal to zero.

Since in this case we have constant annual cash flows,

=> Annual cash flow * PVFA factor = Initial Investment

=> PVFA factor = Initial Investment / Annual cash flow = 75000 / 20806 = 3.6047

Project life = 5 years

We look at PVFA table and in row for 5 years, we get against closest value of PVFA factor = 3.6047, discount %age is = 12%

Hence:

IRR = 12%

Yes, project is acceptable. Since IRR > Cost of capital of 8%

Yes, calculation in this part result in the same number (75000 / 20806 =) 3.6047, which was also calculated in part (a).

In part (a) we calculated to get duration in which we recover the initial investment. In this part we calculated the same as to get the discount rate which the result at which the initial investment equals discounted annual cash flows.

No, it will not happen when annual cash flows are unequal.

Answer (c):

PV factor for annuity for 5 years at 8% rate = (1 - 1/ (1 + 8%) ⁵) / 8% = 3.9927 (upto 4 decimal places)

NPV = Annual cash flow * PVFA - Initial investment

= 20806 * 3.9927 - 75000

= $8072.12

NPV = $8,072.12

Yes, according to NPV rules project is acceptable since NPV > 0