Question

You purchase a first edition of Adam Smith’s The Wealth of Nations today for $100. One year later (year 1), you anticipate you can sell it for $230. One year after that, (year 2), you would have to pay the Australian Tax Office $132 tax on your sale.

a. Find the positive breakeven interest rates on your investment.

b. Determine whether this is a pure investment. (Use only one breakeven interest rate in your calculation – doesn’t matter which one).

c. Your minimum acceptable rate of return (MARR) is 15%. What is the Annual Equivalent (AE) of your two-year investment?

d. Suppose you use the modified internal rate of return MIRR to evaluate investments (instead of using the internal rate of return IRR). Calculate MIRR and determine if you should buy the book. (Note: use MARR when evaluating both cash inflows and cash outflows).

Answer 1

1.
-100+230/(1+r)-132/(1+r)^2=0
Let 1/(1+r) be x
-100+230x-132x^2=0
=>x=5/6,10/11
=>1/(1+r)=5/6,10/11
=>r=1/5,1/10
=>r=20%,10%

2.
Let i be 10%

End Period Cash Flow     Current Balance

0 -100 -100.00
1 230 -100*(1+10%)^1+230 = 120.00 (Note: 1+i = 1+0.10 = 1.1)   
2 -132 120*(1.1)^1-132 = 0.00

An investment is said to be pure if the net present value has a constant sign (positive or negative) at any point during the life of the investment.

Project cash flow balances are greater than 0 when evaluated at i* at any time period.

This is not a pure investment

3.
=(-100+230/1.15-132/1.15^2)*15%/(1-1/1.15^2)
=0.1163

4.
MIRR=((230*1.15)/(100+132/1.15^2))^(1/2)-1=15.0544%

AS MIRR>MARR, accept the project