Financial Concepts

Assignment 7a

Time Value of Money

Instructions

Note: Unless otherwise stated, assume that interest is calculated on an annual basis.

Leave all answers to TWO decimal places.

For the boxes below, put calculator input numbers in the second row and your computed answer in the third row.

Also, observe cash flow sign conventions: negative numbers for outflows [pay, invest, etc.]; positive numbers for inflows [receive, borrow, etc.]

Some additional notes and guidance at the end of the document.

1)Mary has the opportunity to invest $10,000 in a 5 year CD.She has the option to receive a 3.65% return compounded annually; 3.62% compounded quarterly; or 3.60% compounded monthly.What option will give her the highest total return and how much will she receive in 5 years' time? [i.e. find the FVs of each of the options ...]

Also calculate the Effective Annual Rate [EAR] of these of the investment options.

PS: ... the one with the highest FV and EAR is the best investment option.

Annual compounding:

N

i

PV

PMT

FV

EAR

?

?

?

?

= ?

= ?

Quarterly compounding:

N

i

PV

PMT

FV

EAR

Monthly compounding:

N

i

PV

PMT

FV

EAR

2) Using TVM on the financial calculator and the Rule of 72s, how long will it take a $10,000 investment to double if the interest rate is 6.0%? Assume annual TVM compounding.

Using the calculator:

N

i

PV

PMT

FV

Using Rule of 72s: show calculation here ...

What if the TVM compounding is on a monthly basis? Would your answer be the same? Explain by showing calculations below ...

3a)Helen purchases a condoand obtains a $400,000 fully amortizing level payment 30 year mortgage bearing an (annual) [quoted] fixed interest rate of 6.00% [interest compounded monthly].How much will her monthly blended principal and interest payment be? ["blended" refers to calculating your PMT, which in an Amortized Loan, is made up of principal and interest components]

N

i

PV

PMT

FV

[i.e. your calculated PMT above should equal Interest + Amortization of Principal for each period [row] of payment below]

3b) For months 1, 2 and 3 of the mortgage, determine how much of the total payment is principal and how much is interest and construct an amortization table as follows: monkey2

column:[a][b][c][d][e]

= prev row's [e]= PMT from (7a)= [a] x APR 12= [b] - [c]= [a] - [d]

Mth

Beginning

Principal

Payment

Interest

Amortization of Principal

Ending Principal

1

400,000.00

from 7a)

2

from 7a)

3

from 7a)

4) Johnson Corp is considering a Capital Expenditure project that will require an initial investment of $200,000.It will have a 5 year lifetime and will return the following amounts at the end of the following years:

Year 1$20,000

Year 2$30,000

Year 3 $40,000

Year 4$50,000

Year 5$60,000

a) If at the end of year 5, the project has no salvage value, what is the company's expected annual rate of return (IRR)?

Show work below [i.e. fill in the CF numbers below; then use your calculator to get the IRR]:

CF0 = ?, CF1 = ?,CF2 = ?,CF3 = ?,CF4 = ?,CF5 = ?,etc.

IRR = ?

b)If at the end of year 5 the project has a salvage value of $20,000, what is the company's expected annual rate of return?[Hint: The salvage value will add to the cash flow that Johnson receives in year 5; assume no tax on the salvage value]

Show work below [i.e. fill in the CF numbers below; then use your calculator to get the IRR]:

CF0 = ?,CF1 = ?,CF2 = ?,CF3 = ?,CF4 = ?,CF5 = ?,etc.

IRR = ?

c)If the required rate of return of project is 6%, calculate the Net Present Value (NPV) of (a).

Show work below [i.e. fill in the CF numbers below; then use your calculator to get the NPV]:

CF0 = ?,CF1 = ?,CF2 = ?,CF3 = ?,CF4 = ?,CF5 = ?,etc.

I = ?

NPV =