Question

1.) An investment in manufacturing equipment yields the following cash flows for 8 years. At the end of the 8th year the equipment can be sold for $15,000. Assuming an interest rate of 14% (compounded annually), how much would you be willing to invest in this manufacturing equipment?

C=?	I=2000	I=2000	I=2000	I=2000	I=1000	I=1000	I=1000	I=1000	L=$15,000
0	1	2	3	4	5	6	7	8

C: Cost, I: Income, L: Salvage Value

2.) Suppose that the nominal annual interest rate on an investment is 12%. Calculate the effective interest rate if compounding occurs continuously.

3.)

Assume $50,000 is paid for an asset in present time that yields annual cash flow of $6,000 dollars per year in Years 1 through 10, as shown in the table below. At the end of Year 10 the salvage value of the asset is $40,000. Calculate the rate of return on this investment. (In other words, find the value of the interest rate i that makes the Net Present Value of the investment equal to zero - this is also called the Internal Rate of Return.)

A hint here is that you will need to solve this problem either by trial and error or using the IRR function in Excel.

C=-$50,000	I=$6000	I=$6000	I=$6000	...	I=$6000	L=$40,000
0	1	2	3	...	10

Answer 1

Solution 1:

The present value of cash flows, PV is the amount willing to invest in the manufacturing equipment is

PV = 2000/1.14 + 2000/1.14^2 + 2000/1.14^3+2000/1.14^4 + 1000/1.14^5 + 1000/1.14^6 + 1000/1.14^7 + (15000+1000)/1.14^8

PV = 1754.39 + 1538.94 + 1349.94 + 1184.16 + 519.37 + 455.59 + 399.64 + 350.56 + 5258.39

PV = $12,810.96  

Solution 2:

The effective interest rate if compounded continuously is

Effective rate = e^0.12 - 1

Effective rate = 1.1275 - 1

Effective rate = 0.1275 or 12.75%

Solution 3:

Year	CF
0	-50000
1	6000
2	6000
3	6000
4	6000
5	6000
6	6000
7	6000
8	6000
9	6000
10	46000
	10.79%

Using IRR function in excel, we get

IRR = 10.79%