Question

.   Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 8 percent, and that the maximum allowable payback and discounted payback statistic for the project are three and three and a half years, respectively.

Time	0	1	2	3	4	5
Cashflow	-100,000	30,000	45,000	55,000	30,000	10,000

Calculate the payback and use the payback decision rule to evaluate this project; should it be accepted or rejected? Show your calculations.

Answer 1

Payback period is the time taken by the cash inflows to re-earn the initial investment amount. Similarly, discounted payback period is the time taken by the cash inflows DISCOUNTED to time zero, to re-earn the invested amount.

Now, for our question, in order to calculate the discounted payback, we need to calculate the PV of cashflows at time t=0, with 8% discount rate.

Year	Cashflow	Discounted CF formula	Discounted CF
0	(100,000.00)	=-100000/(1+8%)^0	(100,000.00)
1	30,000.00	=30000/(1+8%)^1	27,777.78
2	45,000.00	=45000/(1+8%)^2	38,580.25
3	55,000.00	=55000/(1+8%)^3	43,660.77
4	30,000.00	=30000/(1+8%)^4	22,050.90
5	10,000.00	=10000/(1+8%)^5	6,805.83

Payback Period:

Project earns $75,000 in first 2 years, and hence needs only $25,000 more to re-earn the $100,000 investment amount.

But, the cashflow in year 3 is $55,000, which is $30,000 more than what we require ($25,000). So, we need to find the fraction of year, when we will earn $25,000.

Fraction of year (by extrapolation is): 25,000/55,000 = 0.45 year

Hence, payback period = 2 + 0.45 = 2.45 years

Payback threshold is 3 Years, and the payback period of 2.45 of this project is within the threshold limit. Hence project is acceptible by Payback decision rule.

Discounted Payback Period:

Using the discounted cashflows, Project earns $66,358.02 in first 2 years, and hence needs only $33,641.98 more to re-earn the $100,000 investment amount.

But, the discounted cashflow in year 3 is $43,660.77, which is $10,018.80 more than what we require ($33,641.98). So, we need to find the fraction of year, when we will earn $33,641.98.

Fraction of year (by extrapolation is): 33,641.98/43,660.77 = 0.77 year

Hence, Discounted payback period = 2 + 0.77 = 2.77 years

Discounted Payback threshold is 3.5 Years, and the discounted payback period of 2.77 of this project is within the threshold limit. Hence project is acceptible by Discounted Payback decision rule as well.