Question

Pontification Ltd has a number of investment options however your client has limited these investments to only the following two options: The first investment costs $100,000 and pays the following cash flows in years 3 to 8:Yr 3: $25,000, Yr 4: $30,000, Yr 5: $20,000, Yr 6: $10,000, Yr 7: $50,000 and Yr 8: $80,000.The second investment option costs $250,000 and is a perpetuity which pays $25,000 a year with the 1stcash flow occurring at the end of year 3.Your client indicates that he requires a rate of return of 10% p.a. which can be applied to both of these investments. Identify for him whether these investments are good (or not).

Answer 1

First Investment -

Given,
CF0 = -100000
CF1 = 0
CF2 = 0
CF3 = 25000
CF4 = 30000
CF5 = 20000
CF6 = 10000
CF7 = 50000
CF8 = 80000

Rate of return = r = 0.10

NPV = CF0 + CF1/(1+r) + CF2/(1+r)² +.... + CFn/(1+r)ⁿ

=> NPV = -100000 + 25000/1.1³ + 30000/1.1⁴ + 20000/1.1⁵ + 10000/1.1⁶ + 50000/1.1⁷ + 80000/1.1⁸ = $20314.94

Second Investment -

CF0 = -250000
CF1 = 0
CF2 = 0
CF3 = 25000
CF4 = 25000
.....

Value of Perpetuity in Year 2 = P/(1+r) + P/(1+r)2 + ...... = P/r = 25000/0.10 = 250000

NPV = CF0 + P/(1+r)² = -250000 + 250000/1.1² = $-43388.42

Hence, first investment is a better option since the NPV is greater than zero