Question

What is the present value of the following? 

a. A $500 perpetuity discounted back to the present at 15 percent 

b. A $4,000 perpetuity discounted back to the present at 19 percent 

c. A $100 perpetuity discounted back to the present at 16 percent 

d. A $75 perpetuity discounted back to the present at 12 percent 

a. What is the present value of a $500 perpetuity discounted back to the present at 15 percent? (Round to the nearest cent.) 

b. What is the present value of a $4,000 perpetuity discounted back to the present at 19 percent? $(Round to the nearest cent.) 

c. What is the present value of a $100 perpetuity discounted back to the present at 16 percent? (Round to the nearest cent.) 

d. What is the present value of a $75 perpetuity discounted back to the present at 12 percent? (Round to the nearest cent)

Answer 1

SOLUTION :

a.

Perpetuity of $500 means receiving $500 every year for ever.

Discounting rate , r = 15% = 0.15

PV of $500 perpetuity discounted at 15%

= annuity / r

= 500 / 0.15

= 3333.33 ($) (ANSWER)

b.

Perpetuity of $4000 means receiving $4000 every year for ever.

Discounting rate , r = 19% = 0.19

PV of $4000 perpetuity discounted at 19%

= annuity / r

= 4000 / 0.19

= 21052.63 ($) (ANSWER).

c.

Perpetuity of $100 means receiving $100 every year for ever.

Discounting rate , r = 16% = 0.16

PV of $100 perpetuity discounted at 16%

= annuity / r

= 100 / 0.16

= 625 ($) (ANSWER).

d.

Perpetuity of $75 means receiving $75 every year for ever.

Discounting rate , r = 12% = 0.12

PV of $75 perpetuity discounted at 12%

= annuity / r

= 75 / 0.12

= 625 ($) (ANSWER).

Answer 2

Present Value of Perpetuity = Periodic cash flows divided by the interest rate

	Periodic Cash Flow (A)	Interest Rate (B)	Present Value of Perpetuity (A/B)
a	$        500.00	15%	$    3,333.33
b	$     4,000.00	19%	$ 21,052.63
c	$        100.00	16%	$        625.00
d	$           75.00	12%	$        625.00