Question

BTS corporation has two investment plans A,B and expected to get $1200 of cash flow in 1 year. The investment plan A's β is 1.0 and plan b β is 1.5. If the risk-free interest rate is 10% and market risk premium is 10%, please answer the following question.

Beta fo BTS = (1+1.5)/2 =	1.25
Required return = 10%+1.5*10% =	25.00%
PV for BTS = 1200/1.25 =	$        960.00
Note:
It is assumed that the cash flow of $1,200
is for both the projects put together.
If it is for investment plan, then PV for BTS = 2400/1.25 =	$ 1,920.00

question. explain why the statement is regarded as value additivity principle

Answer 1

Solution:-

Value addivity principle states that the sum of individual values of parts of a group is equal to the value of the group. In the given case, BTS has two investment projects and we are required to calculate the NPV. If the NPV of BTS is equal to the sum of NPVs of the two projects A and B, than it will prove the validity of addivity principle in the given situation.

Beta (A)= 1

Beta (B)= 1.5

Beta (BTS)= (1+1.5)/2= 1.25

As per CAPM model, the required rates of returns for individual projects are calculated as follows:

Required return (A)= 10% + 1*10% = 20%

Required return (B)= 10% + 1.5*10% = 25%

Required return (BTS)= 10% + 1.25*10% = 22.5%

NPV (Project A)= Expected cash flow in 1 year/(100%+Required rate of return)= $1,200/(100%+20%)= $1,000

NPV (Project B)= Expected cash flow in 1 year/(100%+Required rate of return)= $1,200/(100%+25%)= $960

NPV (BTS)= Expected cash flow in 1 year/(100%+Required rate of return)= $2,400/(100%+22.5%)= $1,960

As we can see that the NPV of BTS is equal to sum of the individual NPVs of A and B, thus the statement is regarded as value additivity principle.