TM 661

M2 - Probs II

Consider a simple five year investment project with discrete end-of-year cash flows shown below. Revenue at the end of year one is estimated to be 20,000 which is expected to experience a 10% geometric growth rate so that in year five revenues are estimated to be 29,282. In addition, the project has an estimated salvage value in year 5 of 10,000.

Year Cash Flow 0 $-100,000

1 20,000

2 22,000

3 24,200

4 26,620

5 39,282

Determine the Present Worth equivalent if the value of money is 10% compounded annually.

A bank advertises a certificate of deposit which pays 6% per year. Compute the effective annual interest rate (yield) if the bank

a. compounds monthly.

b. uses continuous compounding.

You are given the following cash flow. You are also given that for a specified MARR of 10%, the Net Present Worth is $40,000.

Period Cash Flow 0 -$250,000 1 40,000 2 60,000 3 A3

4 A4

5 55,000A3 and A4 represent the cash flow streams in periods 3 and 4. These are unknown and are not necessarily equivalent. However, you are also given that at a MARR of 10%, the net present worth (this includes the –250,000 at time 0) of the project is $40,000.

a. Compute the Equivalent Uniform Annual Worth for this cash flow.

You are considering purchasing a bond for $9,000. The bond has a stated face value of $10,000 and pays 6% bond dividends per year. The bond has a remaining life of 5 years at which time the face value of $10,000 will be paid out.

a. Compute the effective interest rate (IRR) earned for the bond. (If you choose to iterate to a solution, you need only show 2 iterations and then indicate how you would find the final solution.)

1 2 3 4 5

600

10,000

9,000

You are given the following cash flow diagram. MARR = 10% per period.

Compute the NPW.

100,000

20,000

10,000

20,000

1 2 3 4 5 6 7 8

K-Corp is considering investing in a machine which costs $40,000. Estimated revenues from the investment (above and beyond additional maintenance costs) are estimated to be $8,000 per year over the 7 year life of the machine. In addition, the machine has an estimated salvage value of $5,000 in year 7. The cash flow is given below.

Compute an equivalent single period at t = 3.

1 2 3 4 5 6 7

8,000

5,000

40,000

Suppose you invest $3,000 per year in a mutual fund that historically earns an average of 10% per year on all monies invested. All money is invested at the start of each year (beginning of period payments).

a. Compute the value of the fund at the end of 30 years.

b. Because of the effects of inflation, you are considering changing mutual funds. If you

desire a real rate of return of 10% after you discount out the effects of inflation, what combined interest rate should you be looking for?