Question

A person has two options for buying an asset: 1) pay £30,000 in cash now or 2) pay £12,000 now, £12,000 in two years and £12,000 in five years. If interest rates were 8% in years one, two and three and 6% in years four and five and there is monthly compounding, which option is better? Please show all work.

Answer 1

The better option is the one that has the lower PV
of the cash outflows:
Option 1:
Present value [no discounting required] =	£     30,000.00
Option 2:
The effective rate of discount for monthly compounding
is to be worked out.
For years 1 to 3, EIR = (1+0.08/12)^12-1 =	8.30%
For year 4 and 5, EIR = (1+0.06/12)^12-1 =	6.17%
The next step is to find the PV of the cash outflows:
12000 paid now [no discounting required]	£     12,000.00
12000 paid in 2 years = 12000/1.083^2 =	£     10,231.15
12000 paid in 5 years = 12000/(1.083^3*1.0617^2) =	£ 8,380.93
Total PV	£     30,612.08
Answer:
The first option is better as the PV of cash outflows is
lower at GBP30,000