Question

A firm purchased $120,000 worth of light general-purpose trucks. The operations of the trucks lead to annual income of $60,000 for years 1~4. These trucks were then sold for $20,000 at the end of year 4. Assume a 30% combined tax rate. With a 40% bonus depreciation plus MACRS depreciation, do the following.
(a) (10 pts) Calculate the before-tax IRR.
(b) (10 pts) Calculate the after-tax IRR.

Answer 1

The before-tax IRR is 37.93%

The after-tax IRR is 19.32%

The internal rate of return (IRR) is defined as the return rate on a project investment project over a periodic lifespan.

It is also referred to as the net present value of an investment project which is zero. It can be expressed by using the formula:

$\mathbf{0= NPV \sum \limits ^{T}_{t=1} \dfrac{C_t}{(1+1RR)^t}- C_o}$

where;

• $\mathbf{C_t}$ = net cash inflow for a time period (t)
• $\mathbf{C_o=}$ Total initial investment cost

(a)

For the before-tax IRR:

The cash outflow = $120000

Cash Inflow for the first three years = $60000

Cash inflow for the fourth year = $60000 + $20000 = $80000

∴

Using the above formula, we have:

$\mathbf{0 = \dfrac{60000}{(1+r)^1}+ \dfrac{60000}{(1+r)^2}+ \dfrac{60000}{(1+r)^3}+ \dfrac{80000}{(1+r)^4}}$

By solving the above equation:

r = 37.93%

(b)

For the after-tax IRR:

The cash outflow = $120000

Recall that:

• Cash Inflow = Cash inflow × Tax rate

∴

For the first three years; the cash inflow is:

$\mathbf{=60000 -(60000\times 0.3) } \\ \\ \mathbf{ = 60000 -18000} \\ \\ \mathbf{ = 42000}$

For the fourth year, the cash inflow is

$\mathbf{=80000 -(60000\times 0.3) } \\ \\ \mathbf{ = 80000 -18000} \\ \\ \mathbf{ = 62000}$

Using the above IRR formula:

$\mathbf{0 = \dfrac{42000}{(1+r)^1}+ \dfrac{42000}{(1+r)^2}+ \dfrac{42000}{(1+r)^3}+ \dfrac{62000}{(1+r)^4}}$

By solving the above equation:

r = 19.32%

Learn more about the internal rate of return (IRR) here:

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