A perpetuity due with annual payments has the following payment pattern: 1, 2, 3, 1, 2,...

Question

Question

A perpetuity due with annual payments has the following payment pattern: 1, 2, 3, 1, 2, 3, ...

Determine the present value of the perpetuity at an annual effective interest rate of 5%.

Answer 1

Answer #1

For payment pattern 1,2,3

Interest Rate = 5%

Calculating Present Value of payment for 3 years

PV at Start = $5.36

Now,

Converting Effective annual rate to rate for 3 year rate as payment repeats its pattern every 3 years,

Effective 3 year interest Rate = (1+0.05)³ -1

Effective 3 year interest Rate = 15.76%

Present Value of Perpetuity = Cashflow/r

Present Value of Perpetuity = 5.36/0.1576

Present Value of Perpetuity = $34.01

Answer 2

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