Question

Find internal rate of return for the project whose cash flows are as flows: 8
Initial investment = Rs.5,00,000
Annual benefit = Rs. 1,50,000
Annual cost = Rs.30,000
Salvage value = Rs. 40,000
MARR = 12% per year

Answer 1

Computing Internal rate of return using trial and error method;

steps;

• Compute Net present value of the project using an arbitrary selected discount rate.
• If the NPV so calculated is positive then try a higher rate and if negative try a lower rate.
• Continue the process until the NPV is equal to zero.
• Use linear interpolation to determine the exact rate

Formulas to be applied are as below,

$pvif= {1 \above{2pt} \left(1+r )^{\smash{n}}\right)}$

$pvifa= {1-(1+r )\left(^{\smash{n}}\right) \above{2pt} r}$

$IRR=Rl+{NPVh*(Rh-Rl) \above{2pt} NPVh+NPVl}$

where

r -rate of return

n -period in years

Rl-lower rate of return

Rh-higher rate of return

NPVh-Net present value using higher rate of return

NPVl-Net present value using lower rate of return

We select arbitrary discount rate, say 20.5% Assuming 10 year of usage.

since year one to year nine cash flows are in annuity,we first calculate NPV for the annuity as follows;

$net cash flow=inflows-annual cost$

$150,000-30,000=120,000$

$pva=120,000*{1-(1+0.205 )\left(^{\smash{9}}\right) \above{2pt} 0.205}=476,085$

we then calculate present value for the 10th year,

$net cash flow=inflows-annual cost +salvage value$

$150,000−30,000+40,000=160,000$

$pv=160,000∗(1+0.205)10)1=24,788$

$NPV=PV cash inflows- PV outflows$

$NPV=476,085+24,788-500,000=874$

NPV using a rate of 20.5% is 874,since it is positive but not large we can try a closer higher rate

remember our target is to have NPV at zero

Lets try 20.6, we apply the same concept as above

$pva=120,000*{1-(1+0.206 )\left(^{\smash{9}}\right) \above{2pt} 0.206}=474,576$

$pv=160,000* {1 \above{2pt} \left(1+0.206 )^{\smash{10}}\right)}=24,576$

$NPV=474,085+24,576-500,000=-848$

NPV using a rate of 20.6% is 848

since we have two rate which are close to zero we can use formula 3 above to calculate the exact IRR

$IRR=20.5+{874*(20.6-20.5) \above{2pt} 874--848} =20.55$

$IRR=20.55\%$