[2] Investment Decisions

Question 1

What does Present Value show?

Answer 1

a measure that expresses these future

revenues in current terms

Question 2

How do we calculate PV when assets provide returns over several periods?

Answer 2

PV = ∑_(𝑡=1)^𝑇〖𝐶_𝑡/((1+𝑟_𝑡 )^𝑡 )=𝐶_1/((1+𝑟_1))+𝐶_2/((1+𝑟_2 )^2 )+𝐶_3/((1+𝑟_3 )^3 )+…+𝐶_𝑇/((1+𝑟_𝑇 )^𝑇 )

where: Ct is the cash flow at period t (assuming that it may vary over time) rt is the rate of the return on the asset at period t (or the opportunity cost of the investment; may also vary over time),
T is the total number of periods during which the asset yields returns.

Question 3

What is the opportunity cost of capital? + eg

Answer 3

The return foregone from a certain investment activity instead of investing to an alternative activity (with the same level of risk).

• If you invest in property instead of buying bonds, then the interest rate on bonds, say r , is the opportunity cost of capital.

Question 4

What is the formula for NPV?

What is the decision rule?

Answer 4

NPV = PV - Cost of Investment

Decision Rule —–> “Accept Investments that yield positive NPV”

Question 5

Ratio of NPV to cost of investment gives what?

Answer 5

Profitability index: Pl = NPV/Q

Question 6

Pitfalls of Profitability index? [4]

Answer 6

• possible bias against costly projects… although they may have a larger NPV.
• resources/funds can be constrained in more periods.
• cannot cope with mutually exclusive projects (eg: require the same piece of land, but different useful life),
• when one project is dependent on another (eg: one is an add-on to the other).

Question 7

Book Rate of Return

Answer 7

Prospective book income as a proportion of the book value of the assets that the firm is proposing to acquire:
BRR = book income book assets

Question 8

Pitfalls of Book Rate of Return measure of a return on investment? [4]

Answer 8

• bias against more costly projects with higher NPV;
• average profitability of past investments is not the right hurdle for new investments;
• depends on which items the accountant treats as capital investment (and how rapidly they are depreciated) and which items are operating expenses;
• therefore, an accountant’s classification of cash flows, may yield different results.

Question 9

What is payback period?

Answer 9

Payback period: measures the number of years it takes for the cumulative cash flow from the project to equal the initial investment.

Question 10

What is the payback rule?

Answer 10

a project should be accepted if its payback period is less than some specific cut-off period.

Question 11

Pitfalls of the payback rule? [2]

Answer 11

all cash flows after the cut-off date are ignored (although they may be significantly high);

all cash flows before the cut-off date are treated equally (without taking account of discounting).

Question 12

What is the internal rate of return? [IRR]
What is it also known as?

What is the rule for if the project should be undertaken?

Answer 12

It is the rate of discount that makes NPV = 0.
It is also called the discounted cash flow rate of return.

if the lRR is greater than the actual opportunity cost of capital (r), i.e. lRR >r =} the project should be undertaken.

Question 13

What is the formula for NPV involving IRR?

What technique is often used ? What are you trying to achieve?

• NPV of a project is steadily declining function of the
  ____ _____.

Answer 13

𝑁𝑃𝑉= T_(𝑡=1) ∑𝐶𝑡/((1+𝐼𝑅𝑅)^𝑡 ) −𝑄=0

Trial and Error to get NPV = 0

Discount rate

Question 14

Pitfalls of IRR? 4

Answer 14

1) in the case of borrowing (positive initial inflow; negative, discounted future outflows) the IRR rule works the other way around, i.e. opportunity cost > IRR
2) when project incurs some future costs, there may be multiple lRRs… or even none!
3) when there are more than one opportunity cost of capital, obtaining the lRR becomes even more complex. Which r do we compare with or weighted av.?
4) it can be misleading with mutually exclusive projects the lRR is unreliable in ranking projects of different scale and with different patterns of cash flow over time.

Question 15

What external factors does IRR ignore?

Answer 15

excludes external factors, such as the risk-free rate, inflation, the cost of capital, or various financial risks

Question 16

What is the rate of return rule?

What is the rule for accepting investments?

Answer 16

The Rate of Return is the ratio of the project’s profitability, the difference between its future cash flows (or payoff) and the cost of investment divided by the cost of the investment.
Denoting the rate of return of an investment by RR, then: RR = (C -Q) / Q

Rate of Return rule: Accept investments that offer rates of return in excess of their opportunity costs of capital, i.e. if RR >r

Question 17

The NPV and RR rules are __________ equivalent.

But we need to be cautious: they are not ______ equivalent!

Answer 17

The NPV and RR rules are, qualitatively, equivalent.

But we need to be cautious: they are not quantitatively equivalent!

Question 18

FINAL THOUGHTS:

The NPV rule, as a means of evaluating and choosing _____ opportunities, is used by a very ____ fraction of firms/CFOs.

The lRR is also preferable to payback, book rate of return and ______ index;

The lRR is less easy to use than the _____ , but, used properly, it gives the ____ _____

Answer 18

investment, large

profitability

NPV, same answer