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