F9 Financial Management

Chapter 5 DCF with Inflation, Taxation and Working Capital

SYLLABUS
1. Apply and discuss the real-terms and nominal-terms approaches to investment appraisal.
2. Calculate the taxation effects of relevant cash flows, including the tax benefits of capital allowances and the tax liabilities of taxable profit.
3. Calculate and apply before- and after-tax discount rates.


1. Inflation

(Pilot, Jun 08, Jun 09, Dec 10, Jun 11, Jun 12, Dec 12, Jun 13, Dec 13, Jun 14, Dec 14, Jun 15, Dec 15)

1.1 Specific and general inflation

1.1.1 It is important to adapt investment appraisal methods to cope with the phenomenon of price movement. Future rates of inflation are unlikely to be precisely forecasted; nevertheless, we will assume in the analysis that follows that we can anticipate inflation with reasonable accuracy.

1.1.2 Two types of inflation can be distinguished.

(a) Specific inflation refers to the price changes of an individual good or service.

(b) General inflation is the reduced purchasing power of money and is measured by an overall price index which follows the price changes of a ‘basket’ of goods and services through time.

Even if there was no general inflation, specific items and sectors might experience price rises.

1.1.3 Inflation creates two problems for project appraisal.

(a) The estimation of future cash flows is made more troublesome. The project appraiser will have to estimate the degree to which future cash flows will be inflated.

(b) The rate of return required by the firm’s security holders, such as shareholders, will rise if inflation rises. Thus, inflation has an impact on the discount rate used in investment evaluation.

1.2 Real and money interest rate

(Pilot, Jun 10, Dec 13)

1.2.1 The money (nominal or market) interest rate incorporates inflation. When the nominal rate of interest is higher than the rate of inflation, there is a positive real rate. When the rate of inflation is higher than the nominal rate of interest, the real rate of interest will be negative.

1.2.2 / Fisher’s (1930) Equation
The generalized relationship between real rates of interest and nominal rate of interest is expressed as follow under Fisher’s equation:
(1 + i) = (1 + r) (1 + h)
Where h = inflation rate
r = real interest rate
i = nominal interest rate
1.2.3 / EXAMPLE 1
$1,000 is invested in an account that pays 10% interest pa. Inflation is currently 7% pa. Find the real return on the investment.
Solution:
Real return = $1,000 × 1.1/1.07 = $1.028. A return of 2.8%.
1.2.4 / Test your understanding 1
If the real rate of interest is 8% and the rate of inflation is 5%, what should the money rate of interest be?
Solution:

1.3 Nominal (money) cash flows and real cash flows

(Jun 13, Dec 13)

1.3.1 We have now established two possible discount rates, the money discount rate and the real discount rate. There are two alternative ways of adjusting for the effect of future inflation on cash flows.

(a) The first is to estimate the likely specific inflation rates for each of the inflows and outflows of cash and calculate the actual monetary amount paid or received in the year that the flow occurs. This is the money (nominal) cash flow.

(b) The other possibility is to measure the cash flows in terms of real prices. That is, all future cash flows are expected in terms of, say, Time 0’s prices. With real cash flows, future cash flows are expressed in terms of constant purchasing power.

1.3.2 / EXAMPLE 2
Storm Co is evaluating Project X, which requires an initial investment of $50,000. Expected net cash flows are $20,000 pa for four years at today’s prices. However these are expected to rise by 5.5% pa because of inflation. The firm’s cost of capital is 15%. Find the NPV by:
(a) discounting money cash flows
(b) discounting real cash flows.
Solution:
(a) Discounting money cash flow at the money rate: The cash flows at today’s prices are inflated by 5.5% for every year to take account of inflation and convert them into money flows. They are then discounted using the money cost of capital.

Note: The question simply refers to the ‘firm’s cost of capital’. You can assume this is the money rate – if you are given a real rate the examiner will always specify.
Time / Money cash flow ($) / Discount rate
@ 15% / PV ($)
0 / (50,000) / 1 / (50,000)
1 / 21,100 / 0.870 / 18,357
2 / 22,261 / 0.756 / 16,829
3 / 23,485 / 0.658 / 15,453
4 / 24,776 / 0.572 / 14,172
NPV = / 14,811
(b)
Calculate the real rate by removing the general inflation from the money cost of capital:
(1 + r) = (1 + i) / (1 + h)
= (1 + 15%) / (1 + 5.5%)
= 1.09
r = 9%
The real rate can now be applied to the real flows without any further adjustments.
Time / Real cash flow ($) / Discount rate
@ 9% / PV ($)
0 / (50,000) / 1.000 / (50,000)
1 – 4 / 20,000 / 3.240 / 64,800
NPV = / 14,800
Note: Differences due to rounding.

1.3.3 In situations where you are given a number of specific inflation rates, the real method outlined above cannot be used.

1.3.4 The following gives a useful summary of how to approach examination questions.

1.3.5 If a question contains both tax and inflation, it is advisable to use the money method.

Multiple Choice Questions
I. Inflation
1. When appraising investment projects using discounted cash flow methods, two approaches to dealing with inflation could be used. These are:
1. to exclude inflation from the estimated future cash flows and to apply a discount rate based on the money cost of capital.
2. to include inflation in the estimated future cash flows and to apply a discount based on the real cost of capital.
Which ONE of the following combinations (true/false) concerning the above statements is correct?
Statement 1 / Statement 2
A / True / True
B / True / False
C / False / True
D / False / False
2. To deal with the effect of inflation when appraising investment projects, two possible approaches can be used. These are:
1. To exclude inflation from the estimated future cash flows and to apply a discount rate expressed in real terms.
2. To adjust the estimated future cash flows by the relevant rates of inflation and to adjust the discount rate to reflect current market rates.
Which one of the following combinations is correct?
Statement 1 / Statement 2
A / True / True
B / True / False
C / False / True
D / False / False
3. The one year rate of inflation is expected to be 3·0%. The one year money rate of interest is 6·3%.
The one year real rate of interest is:
A 3·30%
B 3·20%
C 9·30%
D 9·49%.
4. Dunlin plc is examining an investment opportunity that will lead to savings in staff costs. The company uses the net present value method of investment appraisal based on cash flows expressed in real terms. Staff costs are expected to rise at a rate of 5% each year, whereas the general rate of inflation is expected to rise at a rate of 3% each year. The company has a required rate of return of 10%, assuming no inflation.
What is the appropriate discount rate to use when evaluating the investment opportunity?
A 10%
B 13%
C 13·3%
D 15·5%.
5. Consider the following statements.
When using the net present value method of investment appraisal, the required rate of return from investors is used as the appropriate discount factor. This rate of return should be:
(1) calculated on an after-tax basis
(2) expressed in real terms if the cash flows are expressed in terms of the actual number of dollars to be received.
Which one of the following combinations (true/false) concerning the above statements is correct?
Statement 1 / Statement 2
A / True / True
B / True / False
C / False / True
D / False / False
6. A project consists of a series of cash outflows in the first few years followed by a series of positive cash inflows. The total cash inflows exceed the total cash outflows. The project was originally evaluated assuming a zero rate of inflation.
If the project were re-evaluated on the assumption that the cash flows were subject to a positive rate of inflation, what would be the effect on the payback period and the internal rate of return?
Payback / IRR
A / Increase / Increase
B / Decrease / Decrease
C / Decrease / Increase
D / Increase / Decrease
7. Spotty Ltd plans to purchase a machine costing $18,000 to save labour costs. Labour savings would be $10,000 in the first year and labour rates in the second year will increase by 10%. The estimated average annual rate of inflation is 9% and the company’s real cost of capital is estimated at 10%. The machine has a two year life with an estimated actual salvage value of $5,000 receivable at the end of year 2. All cash flows occur at the year end.
What is the NPV (to the nearest $10) of the proposed investment?
A $50
B $270
C $370
D $1,430
8. A project has an initial outflow at year 0 when an asset is bought, then a series of revenue inflows at the end of each year, and then finally sales proceeds from the sale of the asset. Its NPV is $12,000 when general inflation is zero % per year.
If general inflation were to be rise to 7% per year, and all revenue inflows were subject to this rate of inflation but the initial expenditure and resale value of the asset were not subject to inflation, what would happen to the NPV?
A The NPV would remain the same
B The NPV would rise
C The NPV would fall
D The NPV could rise or fall
9. Data of relevance to the evaluation of a particular project is given below.
Cost of capital in real terms 10% per annum
Expected inflation 5% per annum
Expected increase in the project's annual cash inflow 6% per annum
Expected increase in the project's annual cash outflow 4% per annum
Which one of the following sets of adjustments will lead to the correct NPV being calculated?
Cash inflow / Cash outflow / Discount %
A / Unadjusted / Unadjusted / 10.0%
B / 5% pa increase / 5% pa increase / 15.5%
C / 6% pa increase / 4% pa increase / 15.0%
D / 6% pa increase / 4% pa increase / 15.5%


2. Taxation and Investment Appraisal

(Pilot, Jun 07, Dec 07, Jun 08, Dec 08, Jun 10, Dec 10, Jun 11, Dec 11, Jun 12, Dec 12, Jun 13, Dec 13, Jun 14, Dec 14, Jun 15, Dec 15, Jun 16)

2.1 Tax payable

2.1.1 Taxation can have an important impact on project viability. If management are implementing decisions that are shareholder wealth enhancing, they will focus on the cash flows generated which are available for shareholders. Therefore, they will evaluate the after-tax cash flows of a project.

2.1.2 Payments of tax, or reductions of tax payments, are cash flows and ought to be considered in DCF analysis. Assumptions which may be stated in questions are as follows.

(a) Tax is payable in the year following the one in which the taxable profits are made. Thus, if a project increases taxable profits by $10,000 in year 2, there will be a tax payment, assuming tax at 30%, of $3,000 in year 3.

(b) Net cash flows from a project should be considered as the taxable profits (not just the taxable revenues) arising from the project.

2.2 Capital allowances (tax-allowable depreciation, or writing down allowances (WDAs) or depreciation allowances)

2.2.1 Writing down allowance is used to reduce taxable profits, and the consequent reduction in a tax payment should be treated as a cash saving from the acceptance of a project.

2.2.2 / EXAMPLE 3
ABC Ltd is considering a project which will require the purchase of a machine for $1,000,000 at time zero. This machine will have a scrap value at the end of its four-year life: this will be equal to its written-down value. Inland Revenue Department (IRD) permits a 25% declining balance writing-down allowance on the machine each year. Corporation tax, at a rate of 30% of taxable income, is payable. ABC Ltd’s required rate of return is 12%. Operating cash flows, excluding depreciation, and before taxation, are forecast to be:
Time (year) / 1 / 2 / 3 / 4
$ / $ / $ / $
Cash flows before tax / 400,000 / 400,000 / 220,000 / 240,000
Note: All cash flows occur at year ends.
In order to calculate the NPV, first calculate the annual WDA. Note that each year the WDA is equal to 25% of the asset value at the start of the year.
Years / Annual WDA ($) / Written-down value ($)
0 / 0 / 1,000,000
1 / 1,000,000 × 25% = 250,000 / 750,000
2 / 750,000 × 25% = 187,500 / 562,500
3 / 562,500 × 25% = 140,625 / 421,875
4 / 421,875 × 25% = 105,469 / 316,406
The next step is to derive the project’s incremental taxable income and to calculate the tax payments.
Time (year) / 1 / 2 / 3 / 4
$ / $ / $ / $
Net income before WDA and tax / 400,000 / 400,000 / 220,000 / 240,000
Less: WDA / 250,000 / 187,500 / 140,625 / 105,469
Taxable profit / 150,000 / 212,500 / 79,375 / 134,531
Tax payable at 30% / 45,000 / 63,750 / 23,813 / 40,359