Question

The real interest rate is 5%. What is the value of a new firm which invests 200,000€ initially and expects to have profits (sales minus costs) of 100,000€ next year. 70,000€ the year after, 40,000€ the third year, and then to close down with equipment values at zero? How does your answer change if the equipment bought initially is sold for 50,000€? How does your answer change if the interest rate rises to 10%?

Answer and please provide explanations as well

Answer 1

ANSWER:

There are three parts in the question

1) pw at 5% when initial cost is 200,000 euros.

2) pw at 5% when initial cost is 50,000 euros.

3) pw at 10% when initial cost is 200,000 euros.

profits in year 1 = 100,000 euros

profits in year 2 = 70,000 euros

profits in year 3 = 40,000 euros

1) pw at 5% when initial cost is 200,000 euros = initial cost + profits in year 1(p/f,i,1) +  profits in year 2(p/f,i,2) +  profits in year 1(p/f,i,3)

pw at 5% when initial cost is 200,000 euros = -200,000 + 100,000(p/f,5%,1) + 70,000(p/f,5%,2) + 40,000(p/f,5%3)

pw at 5% when initial cost is 200,000 euros = -200,000 + 100,000 * 0.9524 + 70,000 * 0.9070 + 40,000 * 0.8638

pw at 5% when initial cost is 200,000 euros = -200,000 + 95,240 + 63,490 + 34,552

pw at 5% when initial cost is 200,000 euros = -6,718 euros

so when the initial cost is 200,000 euros with a interest rate of 5% the firm is making a loss of 6,718 euros after 3 years.

2) pw at 5% when initial cost is 50,000 euros = initial cost +  profits in year 1(p/f,i,1) +  profits in year 2(p/f,i,2) +  profits in year 1(p/f,i,3)

pw at 5% when initial cost is 50,000 euros = -50,000 + 100,000(p/f,5%,1) + 70,000(p/f,5%,2) + 40,000(p/f,5%3)

pw at 5% when initial cost is 50,000 euros = -50,000 + 100,000 * 0.9524 + 70,000 * 0.9070 + 40,000 * 0.8638

pw at 5% when initial cost is 50,000 euros = -50,000 + 95,240 + 63,490 + 34,552

pw at 5% when initial cost is 50,000 euros = 143,282 euros

so when the initial cost is 50,000 euros with a interest rate of 5% the firm is making a profit of 143,282 euros after 3 years.

3) pw at 10% when initial cost is 200,000 euros = initial cost +  profits in year 1(p/f,i,1) +  profits in year 2(p/f,i,2) +  profits in year 1(p/f,i,3)

pw at 10% when initial cost is 200,000 euros = -200,000 + 100,000(p/f,10%,1) + 70,000(p/f,10%,2) + 40,000(p/f,10%3)

pw at 10% when initial cost is 200,000 euros = -200,000 + 100,000 * 0.9091 + 70,000 * 0.8264 + 40,000 * 0.7513

pw at 10% when initial cost is 200,000 euros = -200,000 + 90,910 + 57,848 + 30,052

pw at 10% when initial cost is 200,000 euros = -21,190 euros

so when the initial cost is 200,000 euros with a interest rate of 10% the firm is making a loss of 21,290 euros after 3 years.