Q1 Calculate the NPV?

Net Present Value measures the net increase or decrease in the value of the firm by the project which is under consideration. It is calculated as all present value of future cash flows minus cost, i.e.

NPV=Present value of future cash flows - cost

To calculate NPV, we need

Initial Investment (Cost) Required rate of return (on which future cash flows will be discounted) Future cash flows

(a) NPV of modernization the existing paper mill would be

Investment = 154,700,000 Required rate of return =12% Cash flow = 20 year annuity of 40,634,680

NPV = Present value of future cash flows - Investment

NPV = 303,518,451.5 - 154,700,000

NPV = $148,818,451.5

(b) NPV of building a new paper mill would be

Investment = 618,800,000 Required rate of return =12% Cash flow = 20 year annuity of 107,728,000

NPV = Present value of future cash flows - Investment

NPV = 804,668,222.8 - 618,800,000

NPV = $185,868,222.8

This shows that NPV of new facility is higher than that of modernization the existing facility. So, on NPV base, new facility would be better for the firm

Q2

(a) Calculate the IRR of each investment.

IRR is the internal rate of return, it measures the return that an investment can generate over its life. To calculate IRR, we need

Investment Future cash flows

Using the financial calculator, we have calculated the IRR

IRR of investment for modernization the existing facility is 26.01% IRR of investment for new facility is 16.60%

(b) Calculate the Payback of each

Payback is the time period in which investment is recovered.

As both facilities are annuity, so, its payback can be calculated by dividing the investment by yearly cash flow.

Payback of investment for modernization the facility154,700,000/40,634,680 = 3.807 years

Payback of investment for new facility618,800,000/107,728,000 = 5.744 years

On the basis of IRR and payback, modernization the existing facility would be better option as it gives higher IRR and early payback.

Q3

(a) Do the NPV and IRR methods give the same accept/reject signals?

No, NPV favors the new facility whereas IRR favors the modernization the existing facility.

(b) Explain why the NPV and IRR can give divergent signals when evaluating mutually exclusive alternatives.

Mutually exclusive projects are those, whose decision whether acceptance or rejection depends on each other. If one project of mutually exclusive projects is accepted than other would be rejected.

There are two possible reasons for divergent signals when evaluating mutually exclusive alternatives:

1. Investment scale difference2. Cash flows magnitude and timing difference

In this case, both investment scale and magnitude of future cash flows are different. So, this would be the difference.

Q4

If we consider 15 year annuity for modernization the existing facility, its payback would not be affected however, its IRR would decrease by about 1% i.e. 25% and NPV would decrease to 122,057,299.1 but still positive. On the basis of this result, it does not matter much whether existing facility would be for 15 years or 20, because cash flows of latter years has little impact on IRR and NPV and may be no affect on payback. So, it is still better than that of new facility option.

Q5

Based on the calculations, modernization the existing facility would be better option because of its early payback, higher IRR and positive NPV (although less than that of new facility). Based on the information in the case, modernization the existing facility would be again better because new facility location is 15 miles away from the existing facility which would increase the employees' expense and this would be unfair with employees and it may decrease their loyalty for company. So, we recommend to modernize the existing facility.

Q6

(a)

Using the financial calculator, the IRR of this incremental expenditure is 13.26%. This is also known as crossover rate. In mutually exclusive alternatives, if the crossover rate is more than required rate then NPV and IRR methods give different results. However, if crossover rate is less than that of required rate then both NPV and IRR methods give same results.

(b)

On the basis of IRR, proposal will be accepted if its IRR is greater than its cost of capital and rejected if its cost of capital is greater than its IRR. If both proposal have greater IRR than their cost of capital, we would select proposal with higher IRR.

In most cases NPV and IRR gives same decision rule where projects are independent of each other (non mutually exclusive projects) but some time in case of mutually exclusive projects as told above NPV and IRR methods give divergent results. In that case, it is possible that a project with higher IRR may have lower NPV. As NPV is calculated on required rate of return and tells net increase in value is considered better than IRR.

Q7

Yearly cash flow is calculated by using the following data

Modernization the old mill Building a new millInitial Cost 154700000 618800000Working days per year 360 360Tonnage per day 1200 2200Variable cost per ton 282.1 227.5Price per ton 455 455Fixed cost per year 19860000 52200000Tax rate 40% 40%Depreciation SL for 20 years SL for 20 years

Constructing the Income statement (Assuming all produced material will be sold out)

Calculations Modernization the old mill

Building a new mill

Sales Tonnage per day*price per ton*days per year

196560000 360360000

Less:FC &VC FC + VC*tonnage per day*days per year 141727200 232380000EBT 54832800 127980000Less: Tax EBT*40% 21933120 51192000FreeCashFlow 32899680 76788000*Add:Dep Initial cost/20 7735000 30940000NetCash Flow 40634680 107728000

*Depreciation is added back as it is a non cash expense and generated by the project.

Q8

To answer Q8 (a) & (b), we have to calculate the cash flows for each project.

1st 5year cash flows would be:

Modernization the old mill Building a new millSales 196560000 360360000Less: F.C.(dep not included) 12125000 21260000Less: VC 121867200 180180000Dep (SL 5 years) 30940000 123760000EBT 31627800 35160000Less: tax 12651120 14064000Free Cash Flow 18976680 21096000Add: Dep 30940000 123760000Net Cash Flow 49,916,680 144,856,000

Now, the net cash flows for rest of 15 years would be:

Modernization the old mill Building a new millSales 196560000 360360000Less: F.C.(dep not included) 12125000 21260000Less: VC 121867200 180180000EBT 62567800 158920000Less: tax 25027120 63568000Net Cash Flow 37,540,680 95,352,000

Required rate of return and Initial investment is given.

Using the financial calculator, NPV would be

Q8 (a) Modernization the old mill Building a new millNPV 170,320,703.2 271,877,229.6IRR 29.98% 19.74%

Q8 (b) Modernization the old mill Building a new millNPV (dep SL 20 years) 148,818,451.5 185,868,222.8NPV (dep SL 5 years) 170,320,703.2 271,877,229.6NPV change 21,502,251.7 86,009,006.8NPV change % 14.45% 46.32%

The NPV change would be higher in building a new mill, possible reasons would be the magnitude of early and latter cash flows. Latter cash flows experience greater impact of discount rate rather early cash flows. 5 year depreciation makes early cash flows higher.

Q9

The minimum level of annual production below which each proposal would be rejected can be calculated by calculating minimum cash flow required for each proposal throughout its life i.e. 20 years. For that purpose we have to calculate payment (yearly cash flow) by using financial calculator.

FV=0, PV=Investment, I=12%, N=20 & compute pmt= yearly cash flow

Modernization the old Mill Building a new MillYearly Cash Flow 20,711,047.27 82,844,189

This is the minimum cash flow required for each proposal to be accepted, to calculate minimum average annual production, we will construct an income statement in reverse order as follow.

Modernization the old Mill Building a new MillYearly Cash Flow 20,711,047.27 82,844,189Less depreciation 7735000 30940000Net Income 12976047.27 51904189.09EBT (NI/0.6) 21626745.45 86506981.82GP (Add FC) 41486745.45 138706981.8Tonnage per year(GP/P-VC) 239946.4746 609701.019VC per year 67688900.47 138706981.8Sales 109175645.9 277413963.6

Q10

(a)

No, it is not appropriate to judge different proposals on same discount rate because each proposal has its own cost and WACC which is according to its risk. So, in order to evaluate the proposals, we should compare proposal's own WACC with its IRR. If IRR is greater than that of its WACC ( discount rate) Proposal should be accepted otherwise rejected.

(b)

Yes, it is possible that my decision would be change if both projects have different cost of capital. And also it would be easy to decide whether proposal have greater IRR or Cost of capital. If both projects would have higher IRR than their discount rate than I would select project with higher NPV.