12. InvestmentUnder Certainty

IB253 Principles of Finance 1

Lecture 3

Key readingsHillier et al. Appendix 4ABodie et al. 1.1-1.6Copeland, Weston & Shastri 1A-1E, 2A-2B

2

Inter-temporal consumption

How does an investor decide between consuming today and deferring consumption until next period?

Suppose his income is Y0 today and Y1 next period

If investor can lend or borrow at (same) rate R, then he can position himself anywhere on the budget line that passes through (Y0,Y1) with slope (1+R):

10 )(1 YRY ++

Consumptionthis period

Consumptionnext period

Y0

Y1

RY

Y+

+11

0

borrow Y1/(1+R) at rate R+ consume Y0 + Y1/(1+R) now

lend Y0 at rate R+ consume Y0(1+R) + Y1 next period

3Capital Investment

Suppose investor can invest I now in a capital project that will pay C1 for sure next period:

Investor is better off now if net present value:

RY

Y+

+ 11

0

Consumptionthis period

Consumptionnext period

Y0

Y1

Y0-I

Y1+C1

RCYIY

++

+ 111

0

)()(1)( 110 CYRIY +++

011NPV1

011

0 >++

++

+=

RY

YRCY

IY

NPV

4

Consumptionvs. Investment

Rate of return RP on capital project is given by slope (1+RP) of line that joins (Y0,Y1) to (Y0-I,Y1+C1)

If RP>R, capital project adds value

ALL investors will undertake project, regardless of their individual preferences about when to consume their wealth

Consumptionthis period

Consumptionnext period

Y0

Y1

Y0-I

Y1+C1

invest I now in capital projectlend Y0 I at rate Rconsume (Y0-I)(1+R) +Y1+C1 next period

RCY

++

111

invest I now in capital project

borrow at rate R

consume Y0-I + now RCY

++

111

invest I now in capital projectconsume Y0 - I nowconsume Y1+C1 next period

5Fisher Separation

Provided lending and borrowing rates are equal, then all investors agree on whether capital project adds value or not

Criterion for capital investment is that NPV should be positive:

Decision to invest in capital project is separate from consumption decision

individual investor preferences about when to consume do not alter capital investment decision

01NPV1 >

++= R

CI

6

Different lendingand borrowing rates

Fisher separation principle breaks down if lending rate RL and borrowing rate RB are not equal

in real world, RB > RL

If RP > RB > RL,both lenders and borrowerswill invest in capital project

If RB > RP > RL,only lenders will investin capital project

Consumptionthis period

Consumptionnext period

Y0

Y1

Y0-I

Y1+C1

slope RB < RP

slope RL

Consumptionthis period

Consumptionnext period

Y0

Y1

Y0-I

Y1+C1

slope RL

slope RB>RP

7Multi-period case

Assume lending and borrowing rates are equal (to R), so that Fisher separation holds

One-period case

invest if

Multi-period case:

invest if

01NPV1 >

++= R

CI

0)(1...)(1)(11NPVT

33

221 >

+++

++

++

++= TR

CR

CR

CR

CI

C1C2

CT

0

C3

1 2 3 T

I

0 1

I

C1

8

Net Present Value

Net Present Value (or NPV for short) is obtained by

calculating the present value of each cash flow

adding up all of the present values

netting out (i.e. subtracting) initial investment

Present value of individual cash flow Ct is obtained by multiplying the cash flow by the discount factor:

where R is rate at which investors can lend or borrow

Thus far in our story, there is no uncertainty about the size (or timing) of the future cash flows

so R is the rate for riskless lending or borrowing

We will learn later how to adjust R for the fact that future cash flows are risky

tR)(11

+