Question

g Your financial advisor offers you two different investment options. Plan A offers a $17,000 annual payment, in perpetuity. Plan B offers $30,000 annual payments for 18 years. Both plans will make their first payment one year from today. What discount rate would make you indifferent to these two plans

Answer 1

4.76%

Step-by-step explanation:

The requirement in this question is determining the discount rate which gives the same present value in both cases since discount rates discount future cash flows to present value terms.

PV of a pertuity=annual cash flow/discount rate

PV of a pertuity=$17,000/r

PV of ordinary annuity=annual cash flow*(1-(1+r)^-n/r

PV of ordinary annuity=$30,000*(1-(1+r)^-18/r

$17,000/r=$30,000*(1-(1+r)^-18/r

multiply boths side by r

17000=30,000*(1-(1+r)^-18

divide both sides by 30000

17000/30000=1-(1+r)^-18

0.566666667=1-(1+r)^-18

by rearraging the equation we have the below

(1+r)^-18=1-0.566666667

(1+r)^-18=0.433333333

divide indices on both sides by -18

1+r=(0.433333333)^(1/-18)

1+r=1.047554315

r=1.047554315-1

r=4.76%