NewEnvironments:Suppose you have an asset that costs

Suppose you have an asset that costs $15 in time period zero and has an IRR of 12%. With a retained earning rate of 5% on your remaining $7, what is the highest loan rate that would support investing in this asset?

Solution

Initial Cost = IC = $15
IRR = 12%
Retained Earning Rate = RER = 5%
Balance Remaining = BR = $7

The highest blended loan rate we can have is the same as the IRR. The following equation can be set up to solve for the interest rate, i.

IRR = (BR/IC)*RER + ([IC-BR]/IC)*i
Solving for i:

i= [IRR - (BR/IC)*RER]/([IC-BR]/IC)
i= [12% -($7/$15)*5%]/([$15-$7]/$15)

i=18.125%

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