A Good Sample Question

Consider the following

Asset A B C D
Year 0 Cost 10 20 30 40
PW(10%) 16 4 8 88
IRR 17% 15% 11% 6%

MARR = 10%, Loan rate = 7%, Retained earnings = $55

1. Which asset would you get if you had no restrictions on retained earnings if MARR = 10%

Solution:

Asset D because it has the highest PW.

2. Which assets would you get if you had no restrictions on retained earning if MARR = 10%

Solution:

We would get them all because they all have positive present worth’s.

3. If you had $55 of retained earnings and access to a loan rate of 7%, which assets would you get if they are indivisible?

Solution:

Asset A has the highest IRR at 17% which is greater than the MARR at 10% so it is purchased. Asset A can be purchased entirely with retained earnings which leaves us with $45. Next we look at asset B because it has the next highest IRR. Since the IRR is greater than the MARR and year zero cost is $20 we purchase the asset entirely with retained earnings which leaves us with $25 retained earnings. The asset with the next highest IRR is asset C. The IRR of asset C is 11% which is greater than the 10% MARR, but we only have $25 left in retained earnings and the asset costs $30, therefore we would need to take a loan of $5 at 7% to acquire the asset. Calculating the blended incremental rate of return on the cost of funding we get 25/30 (10%) + 5/30 (7%) = 9.5%, which is less than the IRR of asset C, therefore asset C is purchased as well. Asset D is the only asset left and has a positive present worth, but since we have no more retained earnings and the IRR for asset D is less than the loan rate, we do not purchase it with a loan. So we would purchase assets A, B and C.

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