Question

A construction company plans to invest in new equipment to improve their productivity. The planned investment is $500,000 now and $100,000 in year 1.   The gross income for year 1 is $175,000, year 2 is $300,000, and year 3 is $600,000. Taxes related to the investment are $50,000 in year 1, $75,000 in year 2 and $100,000 in year 3.

Determine:

1. The before tax rate of return for the investment
2. The after-tax rate of return for the investment
3. How does the after-tax rate of return compare to the company’s MARR of 15%?

SHOW WORK AND DONT USE EXCEL

Answer 1

Without Excel, we need to use Rate of return (ROR) using Interpolation method as shown.

Using interpolation,

Approximate ROR = RL + [NPVL / (NPVL - NPVH)] x (RH - RL) where

RL: Lower discount rate = 5% (assumed)

RH: Higher discount rate = 10% (assumed)

NPVL: NPV at 5%

NPVH: NPV at 10%

(1) Before-tax:

NPVL = - 500,000 + (175,000 - 100,000) x P/F(5%, 1) + 300,000 x P/F(5%, 2) + 600,000 x P/F(5%, 3)

= - 500,000 + 75,000 x 0.9524 + 300,000 x 0.9070 + 600,000 x 0.8638

= - 500,000 + 71,430 + 272,100 + 518,280

= 361,810

NPVH = - 500,000 + (175,000 - 100,000) x P/F(10%, 1) + 300,000 x P/F(10%, 2) + 600,000 x P/F(10%, 3)

= - 500,000 + 75,000 x 0.9091 + 300,000 x 0.8264 + 600,000 x 0.7513

= - 500,000 + 68,183 + 247,920 + 450,780

= 266,883

So,

Before-tax ROR = 5% + [361,810 / (361,810 - 266,883)] x (10 - 5)%

= 5% + (361,810 / 94,927) x 5%

= 5% + 3.81 x 5%

= 5% + 19.05%

= 24.05%

(1) After-tax:

NPVL = - 500,000 + (175,000 - 100,000- 50,000) x P/F(5%, 1) + (300,000 - 75,000) x P/F(5%, 2) + (600,000 - 100,000) x P/F(5%, 3)

= - 500,000 + 25,000 x 0.9524 + 225,000 x 0.9070 + 500,000 x 0.8638

= - 500,000 + 23,810 + 204,075 + 431,900

= 159,785

NPVH = - 500,000 + (175,000 - 100,000- 50,000) x P/F(10%, 1) + (300,000 - 75,000) x P/F(10%, 2) + (600,000 - 100,000) x P/F(10%, 3)

= - 500,000 + 25,000 x 0.9091 + 225,000 x 0.8264 + 500,000 x 0.7513

= - 500,000 + 22,728 + 185,940 + 375,650

= 84,318

So,

Before-tax ROR = 5% + [159,785 / (159,785 - 84,318)] x (10 - 5)%

= 5% + (159,785 / 75,467) x 5%

= 5% + 2.12 x 5%

= 5% + 10.6%

= 15.60%

(3) After-tax ROR is higher than MARR. So the project is acceptable basis both after-tax and before-tax income.