Question

Cowboy Recording Studio is considering the investment of $143,400 in a new recording equipment. It is estimated that the new equipment will generate additional cash flow of $21,000 per year for each year of its 7-year life and will have a salvage value of $13,500 at the end of its life. Cowboys’s financial managers estimate that the firm’s cost of capital is 8%. Use Table 6-4 and Table 6-5. (Use appropriate factor(s) from the tables provided. Round the PV factors to 4 decimals.)

Required:

A. Calculate the net present value of the investment.

B. Calculate the present value ratio of the investment.

C. What is the internal rate of return of this investment, relative to the cost of capital?

D. Calculate the payback period of the investment.

Answer 1

Given firm's cost of capital = 8%

PVIFA(8%,7years) = 5.20637

PVIF(8%,7th year) = 0.58349

(a) Net Present Value (NPV)

Present value of cash inflow

= Annual Cash inflow x PVIFA(8%,7) + Residual value x PVIF(8%,7)

= 21,000 x 5.20637 + 13,500 x 0.58349

= 109,333.77 + 7,877.115

= 117,210.885

NPV = Present Value of Cashinflow - Present Value of Cash outflow

= 117,210.885 - 143,400

= -26,189.115

(b) Present Value ratio

= Present value of Cashinflow/ Present value of cashoutflow

= 117,210.885/143,400

= 0.81737 or 81.737%

(c) Internal Rate of return

This is the discount rate at which the present value of Cashinflow are equal to present value of cashoutflow. This is the actual rate of return earned by investment.

We can find this ratio using trial and error method.

After trying many rates the final rate at which the present value of Cashinflow and cashoutflow match is 2.723%

(Note : At 3% rate Present value of Cashinflow is 141,814 and at 2.5% rate 144,694. So the interest rate falls between these two. By interpolation we can find the actual rate)

(d) Payback period

This is the period taken by investment to return the investment amount.

21,000 x 6 = 126,000

Remaining investment to be recovered = 143,400 - 126,000

= 17,400

17,400/21,000 x 365 = 302.43

So the Payback period is 6 years and 302.43 days

Note :

No tables for Present value factors are given in question, so taken these from tables available online.

It can also be calculated using formula

PVIFA = Present value interest factor Annuity

= Sum [1/(1+r)^n] (n being 1 to 7 years)

PVIF = Present Value Interest Factor

= 1/(1+r)^n, n is the year 7