Question

Question 21 (4 points) Your significant other just won the Power Ball lottery. S/he has the choice of $10 million today or a 20-year annuity of $700000, with the first payment coming today. What rate of return would make you indifferent between the two alternatives? Your Answer: Answer units

Answer 1

Formula for Present Value annuity due =

1- (1+r)-n - *(1+r)

where, C= Annual payment ;= $700000

r = Interest rate

n= total time period ;= 20

Calculating rate of return:-

700,000 +- (1 + r) **(1+r

Using IRR, taking r= 3%

= 700,000 + [ 1-(140.03)-20 0.03 一 *(1+0.03)

= 10. 726. 660

Using IRR, taking r= 4%

,1- (1 + 0.04) -20 = 700,000 * [? *(1 + 0.04)

=9,893.758

Since, Rate of return would be indifferent between $10 million received today & $700,000 received in 20 years with first payment coming today. So, taking Value of $10 million and putting it in IRR to calculate rate of return.

Rate of Return = Lower rate +[ (NPV at lower rate - NPV)/(NPV at lower rate-NPV at higher Rate)]*(higher rate-lower rate)

= 3 + [(10,726,660 - 10,000,000)/(10,726,660-9,893,758)]*(4-3)

= 3 + [726,660/832,902]*1

= 3.8724%

So, rate of return of 3.8724% will make investor indifferent towards both options.

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