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 7% on the funds,
would your recommendation in part (5.3) change?
Explain.**

Answer #1

lumpsum payment is 24000

future value after 5 years @7% = 24000*1.07^5= 33661

when interest rate is 12% = 24000*1.12^5 = 42296

now we will calculate future value af stream of cash

year | payment | fv factor @ 7% | pv factor @ 12% | fv @7% | fv @ 12% |

1 | 2000 | 1.402551731 | 1.468091531 | 2805.103461 | 2936.183062 |

2 | 4000 | 1.31079601 | 1.37204816 | 5243.18404 | 5488.19264 |

3 | 6000 | 1.225043 | 1.282288 | 7350.258 | 7693.728 |

4 | 8000 | 1.1449 | 1.1984 | 9159.2 | 9587.2 |

5 | 10000 | 1.07 | 1.12 | 10700 | 11200 |

future value | 35257.7455 | 36905.3037 |

when interest rate is 7% stream of cash flows is preffred

when rate is 12% lumpsum is preffred

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that she inherited a few years ago. The buyer is willing to pay R24
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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.
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