1. If your CoC is 10%, what is the present value of $100 in one year's time?

100 ÷ 1.1 = 90.9

2. By how much would this change if your CoC was (a) 5% and (b) 15%?

100 ÷ 1.05 = 95.2 – an increase in value of $4.3m

100 ÷ 1.15 = 87.0 – a decrease in value of $3.9m

Note that although we changed the CoC by ±5% the change in value was not symmetrical.

3. What is the present value of $100 in ten years' time if your CoC was (a) 5%, (b) 10% or (c) 15%?

Discount factors for ten years' time are:

5% CoC Discount factor = 0.614 so present value is 61.4

10% CoC Discount factor = 0.386 so present value is 38.6

15% CoC Discount factor = 0.247 so present value is 24.7

4. An investment offers the potential to earn $10 per annum for the next five years with the first cash flow being in one year's time. If your CoC is 12% what is the maximum amount you should be prepared to pay for the investment?

Discount factors for years 1-5 are: 0.893 0.797 0.712 0.636 0.567

So present value of cash flows is $10m times the sum of these = 36.05

This is the maximum you should be prepared to pay unless there are any other factors to consider that are not mentioned in the question.

[…]