Question

What discount rate would make you indifferent between receiving $3,120.00 per year forever and $5,838.00 per year for 22.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

Answer : Calculation of Discount rate that would make indifferent between receiving $3,120.00 per year forever and $5,838.00 per year for 22.00 years

To find out we need to equate present value of perpertuity and present value of annuity

Present value of perpetuity = Cash Flow / Rate

=$3120 / Rate

Present value of annuity = Periodic payment * [ 1 - (1 + rate)^(-n) ] / Rate

where n is the number of years i.e 22

= $5838 * [1 - (1 + rate)^(-22)] / Rate

Equating both i.e Present value of annuity and Present value of perpetuity

= 5838 * [ 1 - (1 + rate)^(-22)] / Rate =3120 / Rate

= 5838 * [ 1 - (1 + rate)^(-22)] = 3120

==> (3120 / 5838) = 1 - (1 + rate)^(-22)

==> (1 + rate)^(-22) = 1 - 0.53442959917

1 / [(1 + rate)^22] = 0.46557040083

(1 / 0.46557040083) = (1+Rate)^22

==> 1 + rate = (2.14790286972 )^(1 / 22)

Rate = 1.03536 - 1

= 0.03536 or 3.54%