Chapter 4

Question 1

What is the future value of 100 dollar? (The formula)

Answer 1

FV :

100 * (1+r) ^ t

Question 2

What is the basic PV formula?

Answer 2

PV = Ct / (1+r)^t
Ct = cash flow at the end of year t

Question 3

What is the discount factor, and whats the formula?

Answer 3

The discount factor measures the PV of 1 Dollar received in t years:
1 / (1+r)^t

Question 4

Whats the basic NPV formula?

Answer 4

NPV = PV (CFt) - Investment

If positive –> Make the investment, general rule

Question 5

Explain opportunity cost of capital?

Answer 5

The value of the project depends on the timing of cash flows and their risk.
If you believe a project is as risky as investment in the stock market and that stocks offer a 12% expected return, then 12% is the OCC.

Question 6

Whats the other decision rule than the NPV - rule?

Answer 6

Accept if rate of return > OCC.
--> Profit ( NPV) / Investment
E.g:
(420 000 - 370 000) / 370 000 = 0.135
Compare this with OCC, eg 12%.

Question 7

What is the Discounted Cash flow (DCF) formula?

Answer 7

PV = ALLA: Ct / (1+r)^t. This is when there is more than 1 cash flow, meaning that the different streams of money will have different values. Compare the CF year 3 and year 1

Question 8

What is a perpetuity?

Answer 8

A government bond that will not be repaid, but offers a fixed annual income until perpetuity (until its worthless)

Question 9

How is the annual rate of return calculated for a perpetuity?

Answer 9

Cash flows / Present value = r = C / PV

—> PV = C /R

Question 10

How is the PV calculated for an annuity?

Answer 10

PV = (1 / r) - ( 1 / ((r*(1+r)^t)

In case that the first payment starts immidiately, the PV is multiplied by (1+r) also.

Question 11

Whats the PV of a growing perpetuity?

Answer 11

C1 / (1+r) + (C1*(1+g) / (1+r)^t + C1 ( 1+g) ^2 / (1+r)^3
And so on
If g < r, use formula C1 / r-g

Question 12

Calculate EAR (Effective Annual rate)

Answer 12

EAR = [ 1 + (r/m)] ^m   - 1
m = times of payment per year

Question 13

Calculate “book rate of return”

Answer 13

Book Income / Book assets.

It is an average across all the firms activites

Question 14

What is the “Internal rate of return” ? (IRR)

Answer 14

It is the discount rate that makes its NPV = 0

Question 15

How is IRR calculated for a project lasting T years?

Answer 15

NPV = C0 + ( C1 / (1+IRR) + (C2 / (1+IRR) ^2 + …… + CT / (1+IRR) ^T = 0
C0 is a negative, the amount that is invested into the project

Question 16

What is the IRR rule?

Answer 16

Accept an investment project if the OCC is less than IRR

OCC < IRR

Question 17

How is “Profitablity Index” calculated?

Answer 17

Net present value / Investment

Question 18

Whats the 3 generals rules when making investment decisions?

Answer 18

1) Only cash flow is relevant
2 ) Estimate cash flows on an incremental basis
3) Treat inflation consistently

Question 19

What is a “nominal” value?

Answer 19

The real value. E.g if the firm will recieve 200 000 in nominal value in 3 years, the firm will recieve 200 000* (1+r)^3

Question 20

How is the discount rate calculated?

Answer 20

k + g + k*g
g= growth
k = real / nominal interest rate