This document contains several numerical examples calculating present and future values with compound interest, net present value, internal rate of return, payback period, and break-even analysis. It includes calculations for: the future and present value of an investment earning 6% interest compounded annually over 2 years; the present value of $8,000 received in 4 years discounted at 12% annually; the future and present values of a series of payments over 5 years at 12% interest; net present value, internal rate of return, and payback period calculations for an investment project; unit contribution margin and break-even sales volume for a product; and calculations of miles driven and gallons of gas used per year for a vehicle that gets 27 miles per

1. A. FV=PV= 2,000(1+0.06)= $2,120.00 $2,247.20
B. pv = fv/(1+i)n PV OF 8,000X 1/(1+0.12)4= $5,088.00
C. $6,921.61
Year 1 1,754
Year 2 $1,594.39
Year 3 1,350
Year 4 $1,184.16
Year 5 $1,038.74
Total= $6,921.61
D. $32,010.00 at 12%
year 1 $32,010 0.893 $28,584.93
year 2 $32,010 0.797 $25,511.97
year 3 $32,010 0.712 $22,791.12
year 4 $32,010 0.636 $20,358.36
year 5 $32,010 0.567 $18,149.67
year 6 $32,010 0.507 $16,229.07
year 7 $32,010 0.452 $14,468.52
year 8 $32,010 0.404 $12,932.04
Total= $159,025.68

2. a. payback period= intial investment/annual operation cash inflows= 5
b.
c.
26,000/85,000
Accounting rate of return on initial investment= Average annual increase
in net income / Initial investment=30,000(20,000/5)=
30000-(20000/5)
Accounting rate of return on average investment=Average annual
increase in net income/Average investment((15000+30000)/2)=

3. 0.305882353
26,000/150,000= 0.17

4. initial investment.........................................................$(42,070)
Operation
Year 1 ................................................................20,000
Year 2 ................................................................30,000
Year 3 ................................................................10,000
Salvage ................................................................0
a. Year of cash flow Cash Flow
Year 1 20,000
Year 2 30,000
Year 3 10,000
PV $47,377.60
Intital Inesment at time 0 -42,070
Net Presnt Value= $5,307.60
b. Year of cash flow Cash Flow
Year 0 -94,554
Year 1 20,000
Year 2 30,000
Year 3 10,000
IRR -21%

5. Unit selling price ......................................................... $1.45
Variable manufacturing and selling costs ........................ (1.15)
Unit contribution margin ................................................ $0.30
Annual fixed costs
Depreciation (straight-line for 4 years) ......................... $15,000
Other (all cash)......................................................... 30,000
Total…………………………………………………………………………. 45,000
Annual break-even sales volume = $45,000 / $0.30 = 150,000 units

6. a. Payback Period=intital invesment/Annual Operation cash 12,000 miles/27 miles per galon= 444.4444*3
Payback Period= 1600/1400=
b. Year of cash flow Cash Flow
Year 1 1,600
Year 2 1,600
Year 3 1,600
Year 4 1,600
Year 5 1,600
PV $6,388.34
Intital Inesment at time 0 -1,400
Net Presnt Value= $4,988.34
c. 12000 miles per year. It drives 27 miles per galon{444.444}
444.444*4.15 1844.4426

7. es per galon= 444.4444*3.60=1600
1.14