Question

You have just signed a 5-year contract with the ABB Group, a world-famous Engineering Consulting firm. Your compensation includes a $10,000 signing bonus payable today and monthly payments of $6000 at end of the month and an additional $10,000 completion bonus at the end of year 5. Your salary and bonuses are invested in a savings account that pays 4% compounded monthly.

a) What is the present value of this contract?

b) You plan to put both the signing bonus and the completion bonus into a separate savings account (also paying 4% compounded monthly) and use them for a down- payment on your first house in five years. At the end of five years you hope to have accumulated $40,000 for the down-payment, how much additional cash must you put into the separate savings account each month to reach your goal?

c) You found a house that sells for $321,000, put down your $40,000 as a down-pay- ment, and secured a mortgage for the remaining balance. If your mortgage has 20 years of amortization and a quoted mortgage rate of 6% with semi-annual com- pounding, what is your monthly payment?

d) Suppose your friend signed a 5-year contract with another firm. His compensation includes no payments in the first year of the contract and monthly payments at end of each month starting from the second year. His first monthly payment is $10,000 and it grows by 2% (APR compounded monthly) every year until the end of year 5. What is present value of his contract given the same savings interest rate? Does he earn more than you?

Answer 1

a)

Present Value of contract

Rate

Monthly Interest rate=(4/12)

0.3333%

Nper

Number of months=5*12

60

Pmt

Monthly payment

$6,000

Fv

Future Payment(completion bonus)

$10,000

PV

Present Value of Monthly payments and Completion Bonus

$333,984

(Using PV function of excel with Rate=0.3333%, Nper=60,Pmt=-6000,Fv=-10000)

I

Signing Bonus

$10,000

PV+I

Present Value of Contract

$343,984

b)

Savings Required for down payment

Rate

Monthly Interest rate=(4/12)

0.3333%

Nper

Number of months=5*12

60

Pv

Signing bonus

$10,000

FV

Future Value of signing bonus at end of 5 years

$12,210

(Using FV function of excel with Rate=0.3333%, Nper=60,Fv=-10000)

C

Completion Bonus

$10,000

FV+C

Total amount available for downpayment

$22,210

Shortfall in down payment =40000-22210

$17,790

Montthly Savings Required

Fv

Shortfall in down payment at end of 60 months

$17,790

Rate

Interest rate

0.3333%

Nper

Number of months savings

60

PMT

Monthly savings required

$268.33

(Using PMT function of excel with Rate=0.3333%, Nper=60,Fv=-17790)

c)

Monthly Mortgage Payment

Semi annual Interest =6/2=

3%

0.03

Monthly Effective Interest =r

(1+r)^6=1+0.03=1.03

1+r=1.03^(1/6)=

1.004938622

Monthly effective Interest =r=

0.004938622

Rate

Monthly effective Interest =r=

0.4939%

Pv

Mortgage Loan =321000-40000=

$281,000

Nper

Number of months of mortgage =20*12

240

PMT

Monthly Mortgage Payment

$2,001.25

(Using PMT function of excel with Rate=0.4939%, Nper=240,Pv=-281000)