Problem 1 Gene Milton borrowed today a sum of $5,000 from his uncle Ben and at t

Question

Problem 1
Gene Milton borrowed today a sum of $5,000 from his uncle Ben and at the end of year three
paid a sum of $5,000 and paid another $1,000 at the end of year four to pay off the loan.
Determine the interest rate Gene paid it the payments were based on yearly compounding.
A. 6.27% B. 5.93% C. 7.81% D. 8.1%
Problem 2
Consider two mutually exclusive alternatives:
Year X Y
0 -$100 -$50
1 35 16.5
2 35 16.5
3 35 16.5
4 35 16.5
If the minimum attractive rate of return (MARR) is 10%, which alternative should be selected?
A. Alt. X B. Alt. Y C. “Do nothing” D. Both

Explanation / Answer

problem 1) Tee easiest way to find the rate is to use excel: Type the following values into different cells: -5000, 0, 0, 5000, 1000 (this means that he gets 4000 in year 0 then pays nothing the following two years and then 5000 and at the end 1000) to find the rate you press an empty cell and write =irr(and highlight the values you entered) if you entered them in A1 through A5 it should look like this =irr(A1:A5) This is will give you the yearly compounded rate of 5.93%. B) THis can be done as a present value question: option X: investment + yearly cash flow discounted at the rate (10% in this case) raised to the power of the year it occurs in -100 + (35/(1.10^1)) + (35/(1.10^2)) + (35/(1.10^3)) + (35/(1.10^4)) = 10.94 (since this is a positive value you would accept this project because it provides more than 10% return) option y: -50 + (16.5/(1.10^1)) + (16.5/(1.10^2)) + (16.5/(1.10^3)) + (16.5/(1.10^4)) = 2.30 this is also positive so this could also be accepted. Since the projects are mutually exclusive we can only select 1. We should select project X because it creates more value (10.94 compared to 2.30) hope this helps.

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