FINS1613 Business Finance Tutorial Week 7 Solutions

(RTBWJ Chapter 9)

Question 1 Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows. The danger is greatest with a new project because the cash flows are probably harder to predict.

Question 2 With a sensitivity analysis, one variable is examined over a broad range of values. With a scenario analysis, all variables are examined for a limited range of values.

Question 3

Question 4 The base-case, best-case, and worst-case values are shown below. Remember that in the best-case, sales and price increase, while costs decrease. In the worst case, sales and price decrease, and costs increase.

Scenario Unit Sales Unit Price Unit

Variable Cost Fixed Costs

Base case 80,000 $1,280 $340 $5,500,000

Best case 92,000 $1,472 $289 $4,675,000

Worst case 68,000 $1,088 $391 $6,325,000

Question 5 a. We will use the tax shield approach to calculate the OCF. The OCF is:

OCFbase = [(P v)Q FC](1 TC) + TCD OCFbase = [(($36.50 22.75)(95,000)) $830,000](0.70) + 0.30($1,440,000/6) OCFbase = $405,375

Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:

NPVbase = $1,440,000 + $405,375(PVIFA13%,6) NPVbase = $180,506.75

To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 100,000 units. The NPV at this sales level is:

OCFnew = [($36.50 22.75)(100,000) $830,000](0.70) + 0.30($1,440,000/6) OCFnew = $453,500

And the NPV is:

NPVnew = $1,440,000 + $438,250(PVIFA13%,6) NPVnew = $372,888.83

So, the change in NPV for every unit change in sales is:

NPV/S = [($180,506.75 372,888.83)]/(95,000 100,000) NPV/S = +$38.476

If sales were to drop by 500 units, then NPV would drop by:

NPV drop = $35.728(500) NPV drop = $19,238.21

You may wonder why we chose 100,000 units. Because it doesnt matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.

b. To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of $21.75. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $21.75 is:

OCFnew = [($36.50 21.75)(95,000) $830,000](0.70) + 0.30($1,440,000/6) OCFnew = $471,875

So, the change in OCF for a $1 change in variable costs is:

OCF/v = ($405,375 471,875)/($22.75 21.75) OCF/v = $66,500

If variable costs decrease by $1 then, OCF would increase by $66,500.

Question 6 The option to abandon reflects our ability to reallocate assets if we find our initial estimates were too optimistic. The option to expand reflects our ability to increase cash flows from a project if we find our initial estimates were too pessimistic. Since the option to expand can increase cash flows and the option to abandon reduces losses, failing to consider these two options will generally lead us to underestimate a projects NPV.

Question 7 Answer is B

Question 8

Question 9 Expected NPV1 = (30%)($15m) + (40%)($8m) + (30%)($0m) = $7.7m

$7.7

1.10

$7

Question 10

Question 11 Calculate the NPV and the Equivalent Annual Annuity (EAA) of each bus. Choose the bus with the lowest costs. The timeline of the investment opportunity is: 0 1 2 3 4 5 6 7

Old Reliable

200 4 4 4 4 4 4 4

Short & Sweet

100 2 2 2 2

Old Reliable 7

4 1NPV 200 10.11 (1 0.11)

218.85

= +

+

=

Old Reliable7

Old Reliable

EAA 1218.85 10.11 (1 0.11)

EAA 46.44

= +

=

Short and Sweet 4

2 1NPV 100 10.11 (1 0.11)

106.20

= +

+

=

Short and Sweet4

Short and Sweet

EAA 1106.20 10.11 (1 0.11)

EAA 34.23

= +

=

The annual cost of the Short and Sweet bus is less, so they should buy this bus.

Question 12 We need to evaluate the free cash flows associated with each alternative. Note that we only need to include the components of free cash flows that vary across each alternative. For example, since NWC is the same for each alternative, we can ignore it.

The spreadsheet below calculates the relevant FCF from each alternative. Note that each alternative has a negative NPVthis represents the PV of the costs of each alternative. We should choose the one with the highest NPV (lowest cost), which in this case is purchasing the existing machine. 0 1 - 7 8 - 10 Rent Machine 1 Rent (50,000) (50,000) 2 FCF (rent) (35,000) (35,000) 3 NPV at 8% (234,853) Purchase Current Machine 4 Maintenance (20,000) (20,000) 5 Depreciation 21,429 6 Capital Expenditures (150,000) 7 FCF (purchase current) (150,000) (7,571) (14,000) 8 NPV at 8% (210,469) Purchase Advanced Machine 9 Maintenance (15,000) (15,000) 10 Other Costs (35,000) 10,000 10,000 11 Depreciation 35,714 12 Capital Expenditures (250,000) 13 FCF (purchase advanced) (274,500) 7,214 (3,500) 14 NPV at 8% (242,204)

When evaluating a capital budgeting project, financial managers should make the decision that maximises NPV. In this case, Beryls Iced Tea should purchase the current machine because it has the lowest negative NPV.