Question

The following problem is similar, but not identical, to the first question in Problem 5.

What is the present value (PV) today of a stable cash flow of $87,000 per year that starts at the end of year 1 and continues forever (that is, in perpetuity)? The appropriate discount rate is 14% p.a. Round your answer to the nearest dollar. Do not include the $ symbol nor the separating comma, if any. Thus, for example, if the PV is $24,323.55 write 24324 in the answer box.

• The three problems in the text should be straightforward.
• We’ll also solve a more challenging set of problems in class. They pertain to perpetuities in which the periodic payments occur once every several years, and whose initial CF may occur at any time (i.e., it does not necessarily occur at t = 1).

Problem 5 - Perpetuities PV of perpetuity with $100,000/yr, starting in yr 1; r = 10% p.a. C = $ 100,000 10% PV = PV of growing perpetuity with D1 = $50,000, with g = 4% p.a., r= 10% p.a. D1 = $ g= 50,000 4% 10% PV = PV of perpetuity of $100,000/yr, starting in yr 5; r = 10% p.a. $ C = r = S = 100,000 10% 5 years PVS-1 = Note: PVS-1 is the PV of the perpetuity one period (i.e., 1 year in this problem) before the first payment PVO =

Answer 1

Hi

1)Stable cash flow of perpetuity C =$87,000

discount ratw r = 14%

Present Value PV = C/r

= 87000/14% = $621,428.57

5) PV = C/r

= 100,000/10% = $1,000,000

PV of growring perpetuity PV = D1/(r-g)

= 50000/(10%-4%)

= 50000/0.06 = $833,333.33

iii) Since payment is starting in year 5

hence PV in year 4 = 10000/0.1

=$1,000,000

PV0 = 1,000,000/(1+10%)^4

= 1000000/1.1^4 = $6,830,134.55

Thanks