Financial Concepts

Assignment 7a

Time Value of Money

Student Name:

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 condo and 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 rows [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 companys 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 companys 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 = ?

1) What is the current value of a 30-year bond with a 4% coupon rate if the current market interest rate is 5.00%?

N

i

PV

PMT

FV

?

?

?

?

= ?

2) A zero coupon bond is sold at a discount and pays no cash interest during its lifetime. At maturity it pays the face value of the bond.What is the current value of a 10-year zero coupon bond if the current market interest rate is 4.00%? monkey2

N

i

PV

PMT

FV

?

?

?

?

= ?

3) What is the current value of a 20-year bond with a coupon rate of 6% (annual) with semi-annual coupon payments if the current market interest rate is 3.0% (annual)? [The coupon frequency is explicitly stated here because we want to compare this PV(bond) to the next question. Everything else being equal, the frequency of coupons DO affect the price of the bond.]

N

i

PV

PMT

FV

?

?

?

?

= ?

4) What is the current value of a 15-year bond with a coupon rate of 5% with quarterly coupon payments if the current market interest rate is 6.0%?

N

i

PV

PMT

FV

?

?

?

?

= ?

5)What is the Yield to Maturity (YTM) and the Yield to Call (YTC) for a bond which is currently priced at $975 if the bond has a coupon of 6%, matures in 10 years but could be called at a price of $1,025 in 5 years? Spring2 Fall2

Calculate YTM:

N

YTM

PV

PMT

FV

?

?

?

?

= ?

Calculate YTC:

N

YTC

PV

PMT

FV

?

?

?

?

= ?

monkey2

6a) In each of the blue cells below, calculate the value of the respective bonds with various combinations of market interest rate, coupon rate, and maturity assumptions:

[assume annual coupons; $1,000 face value]

[you can leave the following bond prices as positive numbers; easier to calculate % change]

Market Interest Rate = 5%

Maturity

10-Yr

30-Yr

Scenario1

2016 Spring2

1% coupon

What value?

What value?

5% coupon

1,000.00

1,000.00

8% coupon

What value?

What value?

Market Interest Rate = 2%

Maturity

10-Yr

30-yr

Scenario2

1% coupon

What value?

What value?

5% coupon

What value?

What value?

8% coupon

What value?

What value?

In each of the red cells below, calculate the respective change in bond value from Scenario1 to Scenario2:

% change in Bond value from Scenario 1 to 2

Maturity:

10-Yr

30-Yr

1% coupon

% change?

% change?

5% coupon

% change?

% change?

8% coupon

% change?

% change?

6b) What do you conclude about the relative sensitivity of bond prices to changes in interest rate?

[Hint: use the above calculated numbers to make comments on the following comparisons with regard to how sensitive are bond price changes when its market interest rate changes]

1)Longer maturities relative to shorter maturities?

Put your response here .

2)Higher coupon bonds relative to lower coupon bonds?

Put your response here .