Question

Question 1:
a.) Evaluate a 4-year project costing $25,000 and returning $8,000 annually using the payback period technique and a 3-year cutoff. Required Return is 10%.
answer: 3.125 years

b.) Evaluate the Discount Payback Period for the project above.

c.) Evaluate MIRR.

Answer 1

Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 3 + (1000/8000)

= 3.125 years

Since the payback cutoff of the project is 3 years and the actual payback period is more than 3 years, the project must not be accepted.

Note:

Year	Investment	Cash Inflow	Net Cash Flow
0	-25,000.00	-	-25,000.00	(Investment + Cash Inflow)
1	-	8,000.00	-17,000.00	(Net Cash Flow + Cash Inflow)
2	-	8,000.00	-9,000.00	(Net Cash Flow + Cash Inflow)
3	-	8,000.00	-1,000.00	(Net Cash Flow + Cash Inflow)
4	-	8,000.00	7,000.00	(Net Cash Flow + Cash Inflow)

b.

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 3 + (5,105.18407212622 / 5,464.107642921

= 3.93 Years

Since the payback cutoff of the project is 3 years and the actual discounted payback period is more than 3 years, the project must not be accepted.

Note:

	Cash Flow	Discounting Factor ( 10%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-25,000	1	-25,000.00	-25,000.00
1	8,000	0.909090909091	7,272.727272727	-17,727.27272727270000
2	8,000	0.826446280992	6,611.570247934	-11,115.70247933880000
3	8,000	0.751314800902	6,010.518407213	-5,105.18407212622000
4	8,000	0.683013455365	5,464.107642921	358.92357079434000

c. Present value of inflows = 8000* 1/(1.10) ^ 1 +8000* 1/(1.10) ^ 2+8000* 1/(1.10) ^ 3+8000* 1/(1.10) ^ 4

= $ 25,358.92

Future value of inflows = Present value of inflows * ( 1+ Rate of Interest) ^ time

=25,358.92*(1.10)^4

=$37,127.99477

MIRR= [Future value of inflows/Present value of outflow]^(1/n)-1

= [37,127.99477 / 25000] ^ ( 1/4)-1

= 10.39%

Since the MIRR is greater than the required return, the project must be accepted.