Question

Question 5 18 marks
Gina Coulson has just contracted to sell a small parcel of land that she inherited a few years ago. The buyer is willing to pay R24 000 at closing of the transaction or will pay the amounts shown in the following table at the beginning of each of the next five years. Because Gina doesn’t really need the money today, she plans to let it accumulate in an account that earns 7% annual interest. Given her desire to buy a house at the end of five years after closing on sale of the lot, she decides to choose the payment alternative – R24 000 lump sum or mixed stream of payments in the following table – that provides the highest future value at the end of five years.

Mixed Stream
Beginning of Year (t) Cash flow (CFt) (in rands)
1 R2 000
2 4 000
3 6 000
4 8 000
5 10 000

What is the future value of the lump sum at the end of Year 5? (3)
5.2. What is the future value of the mixed stream at the end of Year 5? (5)
5.3. Based on your findings in parts (5.1) and (5.2), which alternative should Gina take? (2)
5.4. If Gina could earn 12% rather than 10% on the funds, would your recommendation in part (5.3) change? Explain. (8)

Answer 1

Solution

1.

Future value = PV*(1+r)^n
=24000*1.07^5=33661.2415368

2.

Future value = CF0*(1+r)^(N-1)+CF1*(1+r)^(N-2)+CF2*(1+r)^(N-3)+CF3*(1+r)^(N-4)+CF4*(1+r)^(N-5)
=2000*1.07^4+4000*1.07^3+6000*1.07^2+8000*1.07+10000=32951.16402

3.

Since the FV of the lumpsum is greater 33661.2415368 than mixed stream, 32951.16402
Choose lumpsum

4.

Future value = PV*(1+r)^n
Future value of lumpsum=24000*1.12^5=42296.2003968

Future value = CF0*(1+r)^(N-1)+CF1*(1+r)^(N-2)+CF2*(1+r)^(N-3)+CF3*(1+r)^(N-4)+CF4*(1+r)^(N-5)

Future value of mixed stream=2000*1.12^4+4000*1.12^3+6000*1.12^2+8000*1.12+10000=35253.15072

Choose lumpsum as still FV of lumpsum > FV of muxed stream

Decision does not change