Question

12. Present values What is the PV of $100 received in: a. Year 10 (at a discount rate of 1%)? b.Year 10 (at a discount rate of 13%)? c. Year 15 (at a discount rate of 25%)? d. Each of years 1 through 3 (at a discount rate of 12%)?

Answer 1

1. Formula for present value calculation

PV = FV / (1+i) ^N

Where,

FV is the future value =$100

Present Value (PV) of the amount =?

i = I/Y = interest rate per year or discount rate = 1%

And N is time period = 10 years

Therefore,

PV= $100 / (1+1%) ^10

= $100 / (1.01) ^10

= $90.53 (rounded off to two decimal points)

2. Formula for present value calculation

PV = FV / (1+i) ^N

Where,

FV is the future value =$100

Present Value (PV) of the amount =?

i = I/Y = interest rate per year or discount rate = 13%

And N is time period = 10 years

Therefore,

PV= $100 / (1+13%) ^10

= $100 / (1.13) ^10

= $29.46 (rounded off to two decimal points)

3. Formula for present value calculation

PV = FV / (1+i) ^N

Where,

FV is the future value =$100

Present Value (PV) of the amount =?

i = I/Y = interest rate per year or discount rate = 25%

And N is time period = 15 years

Therefore,

PV= $100 / (1+25%) ^15

= $100 / (1.25) ^15

= $3.52 (rounded off to two decimal points)

4. PV of annuity formula -

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) =?

PMT = annual payment =$100

n = N = number of payments = 3

i = I/Y = interest rate per year or discount rate = 12%

Therefore,

PV = $100 * [1- (1+12%) ^-3]/12%

= $240.18 (rounded off to two decimal points)