IRR Annuity Problems For each problem, determine the internal rate of return fro

Question

IRR Annuity Problems

For each problem, determine the internal rate of return from the clues. You should have your PV table and a calculator handy for these! Note: the IRR is the rate that makes the PV of the cash flows EQUAL to the investment.

1. Davis Company pays $5,154.2 for a three year annuity of $2,000 each year for 3 years.

    What is the Internal Rate of Return?     %


2. Philips Company pays $12,009 for a three year annuity of $5,000 each year for 3 years.

    What is the Internal Rate of Return?     %


3. Rogers Company pays $24,975.9 for a three year annuity of $9,000 each year for 3 years.

    What is the Internal Rate of Return?     %

Explanation / Answer

This is a typical problem of present value of annuity wherein we need to calculate the rate at which the present value of cash outflows equals the present value of cash outflow.

Formula for present value of annuity

FVOA = A(1 + r)0 + A(1 + r)1 + ...+ A(1 + r)n-1

A = the annuity payment or periodic rent, r = the interest rate per time period, and n = the number of time periods.

The future value of an ordinary annuity (FVOA) is:

Future Value of an

Ordinary Annuity

(FVOA) Formula

FVOA    =             A × (1 + r)^n – 1/r

1.

NPV= Initial cash inflow-cash outflow /(1+r) –cash outflow/1+(1+r)^2-cash outflow/(1+r)^3

IRR is the rate where NPV is zero

i. e. where below condition will be satisfied:

5154.2-(   2000/ (1+r)   +    2000/(1+r)^2    + 2000/(1+r)^3)=0

This will be calculated by using trial and error method.

IRR=8 %

2.

12009-(   5000/ (1+r)   +    5000/(1+r)^2    + 5000/(1+r)^3)=0

IRR=12%

3.

24975.9-(   9000/ (1+r)   +    9000/(1+r)^2    + 9000/(1+r)^3)=0

IRR=4%

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