Question

For project A, the expected investment is $ 1 M and annual Cash Flows are 300K. For project B, the investment is $ 2 M and cash flows are 500K. Economic life for each project is 10 years. Projects are mutually exclusive. a. What is the incremental discounted rate of return? 1. 30% ii. 20% iii. 15% iv, 25%

Answer 1

	Project A	Project B	Incremental CF of B – A
Initial Investment	-1,000,000	-2,000,000	-1,000,000
Cash Flows	300,000	500,000	200,000

a. Incremental discounted rate of return

Using the trial and error method

Life of the projects = 10 years

Let the rate of interest is 14%

At 14% the NPW is

NPW at 14% = -1,000,000 + 200,000 (P/A, 14%, 10)

NPW at 14% = -1,000,000 + 200,000 (5.2161) = 43,220

Since the PW is positive increase the rate of interest to 16% for getting a negative NPW

NPW at 16%

NPW at 16% = -1,000,000 + 200,000 (P/A, 16%, 10)

NPW at 16% = -1,000,000 + 200,000 (4.8332) = -33,360

Using interpolation

Rate of return = 14% + [43,220 – 0 ÷ 43,220 – (-33,360)]*2% = 15.1%

Incremental Discount rate of return will be 15%

Answer – iii. 15%

b. If MARR is 10%, at what year project B will be attractive.

Calculating the discounted payback period of Project B

Year	CF	PV Factor	DCF	CCF
0	($2,000,000)	1	($2,000,000)	($2,000,000)
1	$500,000	0.91	$454,545.45	($1,545,454.55)
2	$500,000	0.83	$413,223.14	($1,132,231.40)
3	$500,000	0.75	$375,657.40	($756,574)
4	$500,000	0.68	$341,506.73	($415,067.28)
5	$500,000	0.62	$310,460.66	($104,606.62)
6	$500,000	0.56	$282,236.97	$177,630.35

Discounted Payback Period = 5 + [-104,606.62 – 0 ÷ -104,606.62 – (177,630.35)]*1 = 5.37 years

Answer – i. 5 years