Question

5. Using a discount rate of 4.8% APR, compounded monthly, calculate the present value of a monthly perpetuity pay‐ ment of $5250 if: (a) the first payment is made one month from now (2 pts.), (b) the first payment is made today (2 pts.), and (c) the first payment is made 30 months from now (2 pts.).

Answer 1

(a) THE FIRST PAYMENT IS MADE ONE MONTH FROM NOW

PRESENT VALUE OF PERPETUAL PAYMENTS = PERPETUAL PAYMENT/(RATE/12)

PRESENT VALUE OF PERPETUAL PAYMENTS = 5250/(0.048/12) = $1312500

ANSWER : $1312500

(b) THE FIRST PAYMENT TODAY

PRESENT VALUE OF PERPETUAL PAYMENTS FROM TODAY= PERPETUAL PAYMENT/( RATE/12) (1 +RATE/12)

PRESENT VALUE OF PERPETUAL PAYMENTS = [5250/(0.048/12)]*(1+0.048/12) = $1317750

ANSWER : $1317750

(c) THE FIRST PAYMENT IS MADE 30 MONTHS FROM NOW

PRESENT VALUE OF PERPETUAL PAYMENTS =

[PERPETUAL PAYMENT/( RATE/12)] [1/(1 +RATE/12)³⁰ ]

PRESENT VALUE OF PERPETUAL PAYMENTS = [5250/(0.048/12)]*[1/(1+0.048/12)³⁰]= $1164318.75

ANSWER : $1164318.75