$($To be completed after Module $1)$

Situation

An investment of $$5500$ for a project lasting four years is anticipated to have revenues of $$3000$ a year for

the first two years and $$2000$ a year for the last two years. Costs are $$500$ for the first year and increase

$$100$ each year for the next two years. There are no costs in the last year. Disposal value is $$1000$ at the

end of four years.

Assignment

Draw the cash flow diagram for this investment.

Prepare a graph with the $"$Y$"$ axis labeled to cover a range from $-$$$6000$ to $+$$$2000$ and label as

"Cumulative NPV$".$ Scale the $"x"$ axis from $0$ to $5$ years. Label horizontal axis "Year".

a$)$ Plot the year by year net "profits" $($costs $-$ revenues$)$ on the graph and join the data points. Determine

the payback period by determining when the plotted line intersects the $$0$ horizontal line. What is the

time required for the net returns to be zero $($revenues $=$ costs$)?$

Note that this is the Payback Period ignoring the interest rate $($i$.$e$.,$ interest rate $=0\%).$

b$)$ Using an interest rate of $20\%,$ find the Net Present Value $($present value of revenues $-$ present value

of costs$)$ of the investment after $0,1,2,3,$ and $4$ years, $($for example, at time $0,$ the NPV would be

$-5500$ ; at time $1$ the NPV would be $(3000-500)*(1\mathrm{.}20{)}^{-1}-5500=-$$$3417$

Plot these on the same graph and join the plotted points.

At what time period does this $20\%$ NPV have a value of $$0?$

Note, this is the Payback period if cost of capital is $20\%$

c$)$ Repeat part b$)$ using an interest rate of $25\%$

$[$The graph you have produced is a RETURN$-$ON$-$INVESTMENT graph showing the recovery of the

initial investment at various rates of interest. This would be a procedure for determining the Payback

Period incorporating an interest rate.$]$

d$)$ From this procedure, there should be an interest rate which would result in a plotted line to pass

through the intersection of $$0NPV$ and Year $4.$ This interest rate is the Internal Rate of Return.

Estimate what this rate would be from your graph. $($i$.$e$.,$ would it be closer to the $20\%$ curve or the

$25\%$ curve?$).$

e$)$ Solve algebraically for the internal rate of return $($or use your IRR key on your SHARP calculator$)$ to

verify your guess in part $d.$