Question

You expect to receive $600 every three months beginning fifteen months from today and expect to receive these payments forever. If the interest rate is 9% EAR, what is this stream of cash flows worth today? （please slso show the resolution using financial calculator)

Answer 1

Sol:

Kindly put the below inputs in financial calculator:

Input - 600

Then press - Division sign

Input - 0.0225 (Interest rate = 9% p.a, Quarterly = 9%/4 = 2.25% or 0.0025)

Then press - Equals sign

You will get the output as 26,666.67

Now,

Input 1 and press N,

Input 11.25 and press I/Y (15 month interest = 9% + (9%/4) = 11.25%)

Input 0 and press PMT

Input -26,666.67 and press FV

Now press CPT and press PV,

You will get the output as 23,970.04

Therefore stream of cash flows worth today is $23,970.04

Alternate method

We first have to compute Present value (PV) of perpetuity.

PV of Perpetuity = Cash flow (Quarterly) / Interest rate (Quarterly) = 600 / 0.0225 = 26,666.67

Now PV of perpetuity should be discounted to determine cash flows worth today.

Cash flow = 26,666.67

Interest rate (r) = (15 month interest = 9% + (9%/4) = 11.25%)

n = 1

PV = Cash flow / (1+r)^{^n}

PV = 26,666.67 / (1+11.25%)^n

PV = 26,666.67 / 1.1125 = 23,970.04