Question

*Two part question

A proposed project has the following costs and benefits:

Year	Costs	Benefits
0	2,000
1		1,000
2		1,000
3		1,000
4		2,000
5		2,000

Assuming an interest rate of 10%, the project's simple payback period is most nearly _________.

	A.	2 years
	B.	4 years
	C.	6 years
	D.	5 years
	E.	7 years

Using the information from the problem above and linear interpolation, the project's discounted payback period is most nearly ___________.

	A.	3.62 years
	B.	2.33 years
	C.	2.05 years
	D.	3.41 years

Answer 1

The information is as under

Year	Costs	Benefits
0	2,000
1		1,000
2		1,000
3		1,000
4		2,000
5		2,000

Calculating the simple payback Period of the investment.

Year	CF	NCF
0	$-2,000	$-2,000
1	$1,000	$-1,000
2	$1,000	$0
3	$1,000	$1,000
4	$2,000	$3,000
5	$2,000	$5,000

It can be seen from the above, it can be seen that the simple payback period is 2 years. At the 2nd year the investor is able to recover the initial cost of 2,000.

Answer – A. 2 years

Calculating Discounted Payback Period

Year	CF	PV Factor	DCF	CCF
0	$-2,000	1	$-2,000	$-2,000
1	$1,000	0.91	$909.09	$-1,090.91
2	$1,000	0.83	$826.45	$-264.46
3	$1,000	0.75	$751.31	$486.85
4	$2,000	0.68	$1,366.03	$1,852.88
5	$2,000	0.62	$1,241.84	$3,094.72

Using linear interpolation, the discounted payback period is

= 2 + [-264.46 – 0 ÷ -246.46 – (486.85)] * 1 = 2.35 years

The discounted payback period is 2.35 years

The closest answer will be B. 2.33 years