, PLEASE USE THIS DOCUMENT AS A GUIDE TO ANSWER YOUR ASSIGNMENT
Question 1
1. Mapex Ltd., a geoinformatics company is expanding into drone manufacturing to diversify its
operations. This project has an initial life of 4 years and the initial costs of the machinery (which
is the only significant initial cost) is R800 000 while the related installation costs is R200 000. The
projects are expected to generate sales of R1 500 000 each year (expressed in real terms).
Variable costs are expected to amount to 60% of sales while fixed costs are expected to be R200
000 (in real terms). The machinery for the project can be depreciated over 4 years and the tax
rate is 27%. The machinery can be sold for R1 200 000 at the end of the project (in nominal
terms). The company is wholly financed by equity. The risk-free rate is 10% and the market risk
premium is 5%. The company currently has a beta of 1.5 while that of the drone industry is 1.5.
Inflation is 4%.
I) Adjusting the cash flows for inflation:
Given that inflation is 4%, adjust certain components of the cash flows, especially the sales revenue
and the terminal value (sale of machinery), to reflect their future values in nominal terms.
Initial Costs:
Machinery cost: R800,000 (no inflation adjustment is needed as this is the initial cost).
Installation cost: R200,000 (also no inflation adjustment, as this is paid upfront).
Revenue (Sales):
Sales are given as R1,500,000 per year in real terms. Since inflation is 4%, adjust these to
nominal terms.
Nominal Sales per year = Real Sales × (1 + Inflation Rate)
So, for each year:
Nominal Sales = 1,500,000 × (1+0.04) = 1,500,000 × 1.04 = R1,560,000 per year
Variable Costs:
Variable costs are 60% of sales, which also needs to be adjusted for inflation.
Nominal Variable Costs = 0.60 × 1,560,000 = R936,000 per year
Fixed Costs:
Fixed costs are already given in real terms as R200,000, so adjust them for inflation.
Nominal Fixed Costs = 200,000 × (1+0.04) = 200,000 × 1.04 = R208,000 per year
Depreciation:
Depreciation is based on the machinery cost and is straight-line over 4 years.
Depreciation is a non-cash expense, so it won't affect nominal cash flows directly but will impact
taxes.
, Terminal Value (Sale of machinery):
The machinery can be sold for R1,200,000 at the end of the project in nominal terms, so no
adjustment for inflation is necessary here.
II) Relevant Cash Flows:
Summarize the key cash flows:
Year 0 (Initial Year):
Initial Investment = R800,000 (machinery) + R200,000 (installation) = R1,000,000 (outflow)
Year 1-4 (Operational Years):
Nominal Revenue = R1,560,000 per year
Nominal Variable Costs = R936,000 per year
Nominal Fixed Costs = R208,000 per year
Depreciation = R200,000 per year
Terminal Year (Year 4):
Sale of Machinery = R1,200,000
Tax:
Taxable Income = Revenue - Variable Costs - Fixed Costs - Depreciation
Taxable Income = 1,560,000 − 936,000 − 208,000 − 200,000 = 216,000
Tax = 27% × 216,000 = R58,320
Net Income = Taxable Income - Tax = 216,000 - 58,320 = R157,680
Cash Flow:
Operating Cash Flow (excluding depreciation) = Net Income + Depreciation
Operating Cash Flow = 157,680 + 200,000 = R357,680 per year (Years 1-4)
Year 4 Cash Flow will also include the terminal value (sale of machinery), so:
Year 4 Cash Flow = 357,680 + 1,200,000 = R1,557,680
III) Determining the Discount Rate (WACC):
Using the CAPM model to calculate the discount rate for the project. The formula is:
Question 1
1. Mapex Ltd., a geoinformatics company is expanding into drone manufacturing to diversify its
operations. This project has an initial life of 4 years and the initial costs of the machinery (which
is the only significant initial cost) is R800 000 while the related installation costs is R200 000. The
projects are expected to generate sales of R1 500 000 each year (expressed in real terms).
Variable costs are expected to amount to 60% of sales while fixed costs are expected to be R200
000 (in real terms). The machinery for the project can be depreciated over 4 years and the tax
rate is 27%. The machinery can be sold for R1 200 000 at the end of the project (in nominal
terms). The company is wholly financed by equity. The risk-free rate is 10% and the market risk
premium is 5%. The company currently has a beta of 1.5 while that of the drone industry is 1.5.
Inflation is 4%.
I) Adjusting the cash flows for inflation:
Given that inflation is 4%, adjust certain components of the cash flows, especially the sales revenue
and the terminal value (sale of machinery), to reflect their future values in nominal terms.
Initial Costs:
Machinery cost: R800,000 (no inflation adjustment is needed as this is the initial cost).
Installation cost: R200,000 (also no inflation adjustment, as this is paid upfront).
Revenue (Sales):
Sales are given as R1,500,000 per year in real terms. Since inflation is 4%, adjust these to
nominal terms.
Nominal Sales per year = Real Sales × (1 + Inflation Rate)
So, for each year:
Nominal Sales = 1,500,000 × (1+0.04) = 1,500,000 × 1.04 = R1,560,000 per year
Variable Costs:
Variable costs are 60% of sales, which also needs to be adjusted for inflation.
Nominal Variable Costs = 0.60 × 1,560,000 = R936,000 per year
Fixed Costs:
Fixed costs are already given in real terms as R200,000, so adjust them for inflation.
Nominal Fixed Costs = 200,000 × (1+0.04) = 200,000 × 1.04 = R208,000 per year
Depreciation:
Depreciation is based on the machinery cost and is straight-line over 4 years.
Depreciation is a non-cash expense, so it won't affect nominal cash flows directly but will impact
taxes.
, Terminal Value (Sale of machinery):
The machinery can be sold for R1,200,000 at the end of the project in nominal terms, so no
adjustment for inflation is necessary here.
II) Relevant Cash Flows:
Summarize the key cash flows:
Year 0 (Initial Year):
Initial Investment = R800,000 (machinery) + R200,000 (installation) = R1,000,000 (outflow)
Year 1-4 (Operational Years):
Nominal Revenue = R1,560,000 per year
Nominal Variable Costs = R936,000 per year
Nominal Fixed Costs = R208,000 per year
Depreciation = R200,000 per year
Terminal Year (Year 4):
Sale of Machinery = R1,200,000
Tax:
Taxable Income = Revenue - Variable Costs - Fixed Costs - Depreciation
Taxable Income = 1,560,000 − 936,000 − 208,000 − 200,000 = 216,000
Tax = 27% × 216,000 = R58,320
Net Income = Taxable Income - Tax = 216,000 - 58,320 = R157,680
Cash Flow:
Operating Cash Flow (excluding depreciation) = Net Income + Depreciation
Operating Cash Flow = 157,680 + 200,000 = R357,680 per year (Years 1-4)
Year 4 Cash Flow will also include the terminal value (sale of machinery), so:
Year 4 Cash Flow = 357,680 + 1,200,000 = R1,557,680
III) Determining the Discount Rate (WACC):
Using the CAPM model to calculate the discount rate for the project. The formula is:
