Question

You are considering two alternate investments – one a perpetuity and the other a stream of uneven cash flows. The perpetuity pays $25,000 in perpetuity from year 6 onwards, while the uneven cash flow investment pays the following cash flows in years 2 to 7: Yr 2: $80,000, Yr 3: $70,000, Yr 4: $60,000, Yr 5: $50,000, Yr 6: $40,000 and Yr 7: $30,000. Required: If you can only buy one of the above investments at a rate of return of 6% per annum, which would you prefer? Which would you prefer if you could achieve a rate of return of 8% per annum? Provide detailed workings.

Answer 1

Find the present value of both the options:

Rate = 6%

Option A,

Present value of perpetuity = Cashflow/Rate

PV at year 6 = 25000/0.06 = 416666.67

PV = 416666.67/(1+0.06)^6 = $293733.56

Option B:

PV = 80000/(1+0.06)^2 + 70000/(1+0.06)^3 + 60000/(1+0.06)^4 + 50000/(1+0.06)^5 + 40000/(1+0.06)^6 + 30000/(1+0.06)^7 = $263011.73

PV is higher for option A, choose option A.

At rate = 8%

Option A,

Present value of perpetuity = Cashflow/Rate

PV at year 6 = 25000/0.08 = 312500

PV = 312500/(1+0.08)^6 = $196928.01

Option B:

PV = 80000/(1+0.08)^2 + 70000/(1+0.08)^3 + 60000/(1+0.08)^4 + 50000/(1+0.08)^5 + 40000/(1+0.08)^6 + 30000/(1+0.08)^7 = $244997.81

PV is higher for option B, choose option B.