Consider a firm with a contract to sell an asset for $151,000 four years from now. The asset costs $96,000 to produce today. a. Given a relevant discount rate on this asset of 13 percent per year, calculate the profit (or loss) the firm will make on this asset. (A loss should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. At what rate does the firm just break even? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

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TomShelby TomShelby · Answer 1 · 2019-09-27T02:55:29+02:00

Answer:

a) loss of 3,388.87

b) it will break even at 11.99%

Explanation:

we will discount the 151,000 at 13% to know the current sales revenue at the sale

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]

Maturity 151,000

time 4 years

rate 0.13

[tex]\frac{151000}{(1 + 0.13)^{4} } = PV[/tex]

PV 92,611.13

the present value is 92,611.13 while the cost is 96,000

there is a loss of 3.388,87‬

To know at which rate the firm break even:

PV = 96,000

[tex]\frac{151000}{(1 + r)^{-4} } = 96,000[/tex]

[tex]\sqrt[-4]{96,000/151,000} - 1 = r[/tex]

r = 0.11989