Question

3. Compounding intervals: Evaluate the following investments. For each, calculate the effective annual interest rates and the FV of $1 invested in each after five years.

   1. An investment with APR = 11% compounded annually.

   2. An investment with APR = 10.7% compounded semi-annually (i.e., twice annually).

   3. An investment with APR = 10.5% compounded continuously.

4. Perpetuities & Annuities:

   1. What is the PV of an asset that pays $10 forever? Assume r = 9%.

   2. How large would the annual payout have to be for 10-year annuity to be worth more than

      the answer to (a)? (You may assume that r is the same.)

   3. An investment costs $1200 down, but will pay $140 in perpetuity. What is the NPV if r =

      10%?

   4. What is the r where NPV = $0?

5. It will cost you $840,000 to buy a factory. Your research shows that it will payoff $210,000 at the end of each year for 10 years. You are a smart person so your opportunity cost of capital is 14%.

   What is the NPV of the factory?

   What could you sell the factory for after 5 years?

DONT DO THEM IN EXCEL PLEASE. I NEED FORMULAS

Answer 1

Effective annual rate =

1. Investment with APR=11% compounded annually

Effective annual rate = (1+11%)-1 = 11%

FV of $1 after 5 years = $1 (1+0.11)^5 = $1.6851

2. Investment with APR=10.7% compounded semi-annually

Effective annual rate = = 10.986%

FV of $1 after 5 years = $1 *  = $1.684

3. Investment with APR=10.5% compounded continuously

Effective annual rate = = 10.71%

FV of $1 after 5 years = $1 * = $1.69046

Perpetuities and Annuities

1. PV of asset paying $10 forever = = $111.11

2. Annual payment = ?

$111.11 =

C = $17.31

3. NPV = -$1,200 + = $200

4.

NPV = $255,380

After 5 years, NPV = -$119,050

So, we will need at least $119,050 to sell the factory