Question

a. Calculate the present value (PV?) of a cash inflow of $500 in one year, and a cash inflow of $1,000 in 5 years, assuming a discount rate of 15%.

b. Calculate the present value (PV?) of an annuity stream of 5 annual cash flows of $1,200, with the first cash flow received in one year, assuming a discount rate of 10%.

c.What is the present value of a perpetual stream of annual cash flows of $100, with the first cash flow to be received in one year, assuming a discount rate of 8%?

d. What is the present value of a perpetual stream of annual cash flows, with the first cash flow of $100 to be received in one year, and with all subsequent cash flows growing at a rate of 3%, assuming a discount rate of 8%?

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Answer 1

a. We need to use the basic time value of money function to calculate the answer to this question. According to th basic TVM function: PV = FV / (1 + r)ⁿ

where FV is future value, PV is present value, r is the discount rate and n is the number of periods.

PV = 434.7826 + 497.1767 = $931.96

b. This is an ordinary annuity, the present value of which can be represented mathematically as:

Here, for our question, P = $1,200, r = 10%, n = 5 years. Substituting the values in formula, we get:

PV = $4,548.94

c. Perpetual cashflows can be discounted and present value for them can be calculated using the formula below:

PV = 100/8%

PV = $1,250

d. This is an example a growing perpetuity, the present value for which can be calculated using the following formula:

PV = 100/(8% - 3%)

PV = $2,000