A buldozer has a purchase cost of 200000 and is expected to

A buldozer has a purchase cost of $200,000 and is expected to last 15 years with no salvage value. Esitmated annual receipts are $40,500, estimated annual average disbursement are $20,900. Compute the rate of return on ownership of this crane.

Solution

Purchase cost = $200000

Estimated annual receipt = $40500

Estimated annual disbursement = $20900

Net annual benefit = $40500 - $20900 = $19600

No. of years = 15

Rate of return = R =?

We have to apply the present value of annuity formula to find the rate of return.

Purchase cost = Present value of all net annual benefits

Present value of all net annual benefits = Net annual benefit *(1-1/(1+R)^n)/R

Present value of all net annual benefits =19600*(1-1/(1+R)^15)/R

At R = 6%

Present value of all net annual benefits = $190360.08

At R = 5%

Present value of all net annual benefits =$ 203441.30

Thus, by the method of interpolation:

Rate of Return = 5% + ((PV at 5% - 200000)/ (PV at 5% - PV at 6%))*(6% - 5%)

Rate of Return = 5% + ((203441.30 - 200000)/ (203441.30- 190360.08))*(6% - 5%)

Rate of Return = 5.26% approx.