Question

A- Annuity Present Value -You are looking into an investment that will pay you $12,000 per year for the next 10 years. If you require a 15 percent return, what is the most you would pay for this investment?

B- Describe how to calculate the future value of a series of cash flows.

C- Describe how to calculate the present value of a series of cash flows.

Answer 1

A)

The most we can pay is nothing but the present value of of all the cash inflows.

We know the formula for present value of an annuity is.

Present value of annuity - P*((1-(1+r)^-n)/r

Where P = Equalised periodic payment

r = rate of interest

n = Number of periods'

Given that the Annual Equalised investment is $12,000

N = 10 years r =15%

Let us substitute this in the above formula .

Accordingly we get the following 12,000 * (1-(1.15)^-10)/0.15

= 12000 * (1- 0.247185)/0.15

= 12000 * (0.752815)/0.15

= 12000 * 5.018769

= 60225.22

Hence the highest amount we can pay is $60225.22.

= 70168.44

Hence the most we can pay is $70168.44

B)

Future value of cash flows is calculated using the compounding factor for each cash flows till the period we need the future value

For example we need the future value of $ 100 Today in 2 years at a rate of 14%

Hence Future value will be 100 * (1.14)² = 129.96

For the above annuity we can calculate future value as per the below tabe.

Year	Cash flow	Compounding Factor	Future Value
1	12000	3.5179	42,214.5
2	12000	3.0590	36,708.3
3	12000	2.6600	31,920.2
4	12000	2.3131	27,756.7
5	12000	2.0114	24,136.3
6	12000	1.7490	20,988.1
7	12000	1.5209	18,250.5
8	12000	1.3225	15,870.0
9	12000	1.1500	13,800.0
10	12000	1.0000	12,000.0

C ) Similarly present value of a series of cash flows will be calculating by discounting each cash flow with the present value factor

For example - We get $100 in 2 years and the relevant interest rate is 10%

Hence the present value will be 100/(1.1)²

= 82.64463

The below table can better explain the present value of annuity we computed in the first part.

Year	Cash flow	Compounding Factor	Future Value
1	12000	0.870	10,434.783
2	12000	0.756	9,073.724
3	12000	0.658	7,890.195
4	12000	0.572	6,861.039
5	12000	0.497	5,966.121
6	12000	0.432	5,187.931
7	12000	0.376	4,511.244
8	12000	0.327	3,922.821
9	12000	0.284	3,411.149
10	12000	0.247	2,966.216

IF we add all the future values we get the value we got in part A that is $60225.224