4) Solve the following questions involving Internal Rates of Return and perpetui

Question

4) Solve the following questions involving Internal Rates of Return and perpetuities.

a) For investment of $250m today an investor can receive $30m at the end of each year starting in

one year and continuing forever. Find the IRR.

b) For investment of $200m today an investor can receive $2m at the end of each month starting in

one month and continuing forever. Find the IRR.

c) For an investment of $200 million today an investor will receive annual payments starting at $X in

one year and decreasing by 5% every year. If the investor wants t an IRR of at least 12%, find the

minimum value of X that will meet this goal.

d) For an investment of $40 today an investor will receive annual income starting with a payment of

$1 in one year and increasing by $1 every year. Find the IRR.

Explanation / Answer

1
0=-250+30/(1+IRR)+30/(1+IRR)^2........
0=-250+30/IRR
=>IRR=30/250=12%

2
0=-200+2/(1+IRR/12)+2/(1+IRR/12)^2........
0=-200+24/IRR
=>IRR=24/200=12%

3
0=-200+X/(1+IRR)+X*(1-5%)/(1+IRR)^2.........
0=-200+X/(1+IRR)/(1-0.95/(1+IRR))
0=-200+X/(IRR+0.05)
IRR=X/200-0.05
GIven, IRR must be at least 12%
So, X/200-0.05>0.12
=>X>34
4
S1=0=-40+1/(1+IRR)+2/(1+IRR)^2+3/(1+IRR)^3
Dividind S1 by 1+IRR, we get S2=0=-40/(1+IRR)+1/(1+IRR)^2+2/(1+IRR)^3........
S1-S2=-40+41/(1+IRR)+1/(1+IRR)^2+1/(1+IRR)^3........
0=-40+41/(1+IRR)+1/(1+IRR)^2+1/(1+IRR)^3........
0=-40+41/(1+IRR)+1/((1+IRR)*IRR)
Hence, IRR=17.1106420114811%

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