Question

Consider a business loan maturing in three years that has three remaining annual payments in one, two, and three years. The annual payments are all equal to $3 Million. While analyzing the loan, you are using a YTM equal to 10%.

Determine the duration of the loan and then, using this estimated duration and a duration analysis, predict the percentage change in the value of the loan after a 0.5 percentage point increase in the interest rate. You should assume that a one percentage point change in the rate is approximately equal to a one percent change in the rate.

Answer #1

Year | Cashflow(million) | PV @10 | PV | Proption of bond value | Propotion of Bond value *Time(yars) |

1 | 3 | 0.909 | 2.727 | 0.365544698 | 0.365544698 |

2 | 3 | 0.8264 | 2.4792 | 0.332327985 | 0.66465597 |

3 | 3 | 0.7513 | 2.2539 | 0.302127317 | 0.906381952 |

7.4601 |
1 |
1.93658262 |

Duration Years = | 1.936583 | ||

Volatility = | Duration / (1+YTM) | ||

1.936583/1.10 | |||

1.76053 |
|||

1.76 |

Value of loan if interest rate incfreases to .5 percentage point
thevalue of loan will decrease by .5*1.76 = **.88
%**

(excel) Consider a 8% coupon bond
making annual coupon payments with 4 years until maturity
and a yield to maturity of 10%.
What is the modified duration of this bond?
If the market yield increases by 75 basis points, what is the
actual percentage change in the bond’s
price? [Actual, not approximation]
Given that this bond’s convexity is 14.13, what price would you
predict using the duration-with-convexity
approximation for this bond at this new yield?
What is the percentage error?

Find the duration of a 8% coupon bond making annual
coupon payments if it has three years until maturity and a yield to
maturity of 7.8%. What is the duration if the yield to maturity is
11.8%? (Do not round intermediate calculations. Round your
answers to 4 decimal places.)
YTM
Duration
7.8% YTM
11.8% YTM

Find the duration of a 6% coupon bond making annual coupon
payments if it has three years until maturity and a yield to
maturity of 7.7%. What is the duration if the yield to maturity is
11.7%? (Do not round intermediate calculations. Round your answers
to 4 decimal places.)
YTM Duration 7.7% YTM 11.7% YTM

Find the duration of a 8% coupon bond making annual
coupon payments if it has three years until maturity and a yield to
maturity of 7.8%. What is the duration if the yield to maturity is
11.8%? (Do not round intermediate calculations. Round your
answers to 4 decimal places.)
YTM
Duration
7.8% YTM

1.You are borrowing $100,000 for an amortized loan with terms
that include annual payments,6 year loan, and interest rate of 4.5
per year. How much are your equal annual
payments? Answer to the nearest cent xxx.xx, and do not
enter the dollar sign.
2.Calculate the total present value of the following three cash
flows: $15 obtained one year from today, $24 obtained
two years from today, and $30 obtained three years from
today. Use 6.7% as the interest rate. Answer
to the nearest cent, xxx.xx and...

An industrial bank will loan you $20,500 for three years to buy
miscellaneous equipment for your firm. The loan must be repaid in
equal monthly payments. The annual interest rate on the loan is
8.5% of the unpaid balance. How large are the monthly payments?

A 6% coupon bond is making annual coupon payments and has a
duration of 8 years. What will be the percentage change in the
bond's price if its yield to maturity changes from 6% to 6.1%?

A loan has a stated annual rate of 17.9%. If loan payments are
made monthly and interest is compounded monthly, what is the
effective annual rate of interest? (Show your answer to the fourth
decimal place, as a decimal, NOT as a percentage. DO NOT round
until after all calculations have been completed and you have
reached your final answer.)

5. You have a $ 6,000 loan to be repaid in 5 years (annual
payments) at a 7% interest rate. Create an amortization schedule
for a fully amortized loan with constant-payment installments.

Construct an amortization schedule for a $1,000, 8% annual rate
loan with 3 equal payments. The first payment will be made at the
end of the1st year. Find the required annual payments
$355.8
$367.2
$388.0
$390.7
Based on the information from above, what’s the ending balance
of the amortized loan at the end of the second year
$0
$359.4
$388.3
$682.8
Based on the information from above, calculate the total amount
of interests you should pay for the amortized loan...

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