Question

Time    Cash flow

0    -165,000

1 56,500

2    67,400

3    45,600

4 29,800

5 7,500

Suppose your firm is considering investing in Project K with the cash flows shown in the table. Assume that the required rate of return on projects of this risk class is 7.5 percent, and that the maximum allowable payback and discounted payback statistics for the project are 3.0 and 3.6 years, respectively. Which of the following statements is (are) correct?

(x) If you use the payback decision rule to evaluate this project then you accept the project since the payback period is 2.9 years.

(y) If you use the discounted payback decision rule to evaluate this project then you reject the project since the discounted payback period is 3.8 years. (z) The NPV of this project is more than $10,000. If you use the NPV decision rule to evaluate this project; then it should be accepted.

Answer 1

(x) First of all lets calculate payback period:

Year	Cash Flows	Cumulative Cash Flows	Cumulative cash flows calculation
0	(165000)	(165000)	(Year 0 cash flows)
1	56500	(108500)	(Year 0 cash flows + Year 1 cash flows)
2	67400	(41100)	(Year 0 cash flows + Year 1 cash flows + Year 2 cash flows)
3	45600	4500	(Year 0 cash flows + Year 1 cash flows + Year 2 cash flows + Year 3 cash flows)

Since in the year between 2 and 3 we get a cumulative cash flow equal to 0, it means that the payback period is in between 2nd and 3rd year, Payback period is calculated by using the below function:

= 2 years + 2nd year cumulative cash flow in positive sign (since the payback period is in between 2nd and 3rd year) / Next years cash flow (i.e. 3rd year cash flow)

= 2 years + 41100 / 45600

= 2.90 years (Approximately)

Hence we can accept the project since the payback period is within the maximum allowable payback period, hence statement (x) is correct.

(y) Now, we shall calculate the discounted pay back period as follows:

Year	Cash Flows (1)	Discount Factor (2)	Discounted Cash Flows (1 x 2)	Cumulative discounted cash flows
0	(165000)	1	(165000)	(165000)
1	56500	1 / 1.075 = 0.93	52545	(112455)
2	67400	1 / 1.0752 = 0.87	58638	(53817)
3	45600	1 / 1.0753 = 0.80	36480	(17337)
4	29800	1 / 1.0754 = 0.75	22350	5013

Cumulative discounted cash flows are calculated by taking the sum of discounted cash flows

Since in the year between 3 and 4 we get a cumulative cash flow equal to 0, it means that the discounted payback period is in between 3rd and 4th year, Discounted payback period is calculated by using the below function:

= 3 years + 3rd year cumulative cash flow in positive sign (since the discounted payback period is in between 3rd and 4th year) / Next years cash flow (i.e. 4th year cash flow)

= 3 years + 17337 / 22350

= 3.8 years (Approximately)

Hence we can't accept the project since the discounted payback period is more than the maximum allowable discounted payback period, hence statement (y) is correct.

(z). Now, we shall calculate the project's NPV as follows:

= Initial cash outflow + 1st year inflow / ( 1 + required rate of return )¹ + 2nd year inflow / ( 1 + required rate of return )² + 3rd year inflow / ( 1 + required rate of return )³ + 4th year inflow / ( 1 + required rate of return )⁴ + 5th year inflow / ( 1 + required rate of return )⁵

= (165000) + 56500 / (1.075)¹ + 67400 / (1.075)² + 45600 / (1.075)³ + 29800 / (1.075)⁴ + 7500 / (1;.075)⁵

= 10,126 Approximately   

Since the NPV is more than 10,000 which is more than NPV required in the question, hence the project can be accepted. So statement z is also correct.

So, we can conclude all the three statements are correct.