Question

Suppose you are offered an investment opportunity that will pay you ​$5352.41 per month for 48 months. To make this​ investment, you must invest a total of ​$175000​, but only ​$17500 is in cash at the start. You must borrow the rest of the investment ​($157500​) from​ Lo-Rate Bank at 18​% ​APR, with monthly​ compounding, and the entire loan must be repaid at the end of the 48 months in one lump​ sum, which will total ​$321847.83. To be​ clear, absolutely NO repayment of the loan before the end of the 48 months is allowed. This investment is completely riskless and there are no taxes. What is the minimum APY you would need to be able to earn from reinvesting all the monthly income to make this a​ zero-NPV investment? ​ (Percent with 2​ decimals.)

Answer 1

In this question we need to calculate the RATE of return that this company need to earn to make the NPV zero.

Given

PMT (Earning per Month) = $5352.41

Nper (Period in Months) = 48

FV (Future Value that need to Pay) = $321847.83+$17500 = $339,347.83 (Because $17500 is also investing in this project therefore to make this project NPV zero that amount also need to consider)

Present Value (PV) = 0

Now use the formula of Rate in excel

$=Rate(nper,PMT,PV,FV)$

$=RATE(48,-5352.41,0,339347.83)$

$RATE = 1.1384\% Per Month$

So company need to earn 13.66% PA (1.1384*12) to make this a ZERO NPV Investment.

I hope this clear your doubt.

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