Question

Consider a firm with a contract to sell an asset for $154,000 five years from now. The asset costs $90,000 to produce today. Given a relevant discount rate of 13 percent per year, calculate the profit the firm will make on this asset. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Firm's profit(loss) $ At what rate does the firm just break even? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Break-even rate

Answer 1

Answer:

the firm will have a loss of 6.414,97‬

Break-even rate = 11.34%

Explanation:

We calcualte the present value of a lump sum to know the present sale value:

$\frac{Nominal}{(1 + rate)^{time} } = PV$  

Nominal:  154,000

time               5 years

rate               0.13

$\frac{154000}{(1 + 0.13)^{5} } = PV$  

PV   83,585.03

the current sale price        83,585.03

given a cost of                 (90,000)      

the firm will have a loss of 6.414,97‬

To break event the present value should be 90,000:

$\frac{154000}{(1 + r)^{5} } = 90,000$

$\sqrt{5}{\frac{154000}{90,000}} -= (1 + r)$  

rate = 0.113411345 = 11.34%