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# Start Up Company Finance Calculations

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3.4) A start-up company selling color-keyed carnauba car wax borrows \$40,000 at an interest rate of 10% per year and wishes to repay the loan over a 5-year period with annual payments such that the third through fifth payments are \$2000 greater than the first two. Determine the size of the first two payments.

3.11) How much money would you have pay each year in 8 equal payments, starting 2 years from today, to repay a \$20,000 loan received from a relative today, if the interest rate 8% per year?

3.14) The operating cost of a pulverized coal cyclone furnace is expected to be \$80,000 per year. If the steam produced will be needed only for 5 years beginning now (i.e., years 0 through 5), what is the equivalent annual worth in years 1 through 5 of the operating cost at an interest rate of 10% per year?

3.16) The first phase will reduce labor and travel costs by \$28,000 per year. The second phase will reduce costs by an additional \$20,000 per year. If phase I savings occur in years 0, 1, 2 and 3 and phase II occurs in years 4 through 10, what is the equivalent annual worth of the upgraded system in years 1 through 10 at an interest rate of 8% per year?

3.20)Calculate the future worth (in year 11) of the following income and expenses, if the interest rate is 8% per year.

YEAR INCOME EXPENSE
0 12,000 3000
1-6 800 200
7-11 900 200

3.37) Operating cost per machine is \$22,000 per year for years 1 and 2 and then it increases by \$1000 per year through year 5, what is the equivalent uniform annual cost per machine (years 1 through 5) at an interest rate of 12% per year?

3.44) Calculate the present worth (year 0) of a lease that requires a payment of \$20,000 now and amounts increasing by 5% per year through year 10. Use an interest rate of 14% per year.

3.53) Compute the future worth in year 10 at i=10% per year for the cash flow shown below.

See attached file for full problem description.

#### Solution Preview

3.4) A start-up company selling color-keyed carnauba car wax borrows \$40,000 at an interest rate of 10% per year and wishes to repay the loan over a 5-year period with annual payments such that the third through fifth payments are \$2000 greater than the first two. Determine the size of the first two payments.

Year 0 1 2 3 4 5
(40,000) x x 2,000 + x 2,000 + x 2,000 + x

We can find the size of the payments as follows: -
Let x = size of the first two payments

PVIFA = 1 - 1 where PVIFA is the present value of a regular annuity factor
(1 + i)n i is the interest rate
i n is the period

PVIF = 1 where PVIF is the present value factor
(1 + i)n

PV = X(PVIFA10%, 5) + 2,000(PVIFA10%, 3)(PVIF10%, 2)
40,000 = X(3.7908) + 2,000(2.4869)(0.8264)
40,000 = 3.7908X + 4,110.35
35,889.65 = 3.7908X
X = 9,467.57

3.11) How much money would you have pay each year in 8 equal payments, starting 2 years from today, to repay a \$20,000 loan received from a relative today, if the interest rate 8% per year?

Year 0 1 2 3 4 5 6 7 8 9
(20,000) x x x x x x x x

PV = X(PVIFA8%, 8)(PVIF8%, 1)
20,000 = X(5.7466)(0.9259)
20,000 = 5.3208X
X = ...

#### Solution Summary

This solution is comprised of a detailed explanation and calculation to determine the size of the first two payments for a start-up company.

\$2.19