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# Present value and arbitrage opportunity

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1. Having \$200 in one year is equivalent to having what amount today?
\$218.08
\$408.00
\$192.31
\$208.00
\$800.00
2. Which would you prefer, \$200 today or \$200 in one year? Does your answer depend on when you need the money? Why or Why not?

3.What is the no-arbitrage price of a security that pays cash flows of \$100 in one year and \$100 in two years?
\$189.00
\$519.00
\$132.00
\$179.00
\$130.00

4. What is the no-arbitrage price of a security that pays cash flows of \$100 in one year and \$500 in two years?
\$189.00
\$519.00
\$132.00
\$179.00
\$130.00

5. Suppose a security with cash flows of \$50 in one year and \$100 in two years is trading for a price of \$130. What arbitrage opportunity is available?

13. The British government has a consol bond outstanding paying 100 pound per year forever. Assume the current interest rate is 4% per year. What is the value of the bond immediately after a payment is made?

Ans. ______________

14. The British government has a consol bond outstanding paying 100 pound per year forever. Assume the current interest rate is 4% per year. What is the value of the bond immediately before a payment is made?

18. Oppenheimer Bank is offering a 30-year mortgage with an EAR of 5 3/8%. If we plan to borrow \$150,000, what will our monthly payment be?

Ans. ______________

19. You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is \$2,356 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6 3/8% (APR). How much do you owe on the mortgage today?

Ans. ______________

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#### Solution Preview

1. Having \$200 in one year is equivalent to having what amount today?
\$218.08
\$408.00
\$192.31
\$208.00
\$800.00

This will depend on the interest rate. Here we assume it to be say 4%.
Then the Present value of \$200= Future value/(1+interest rate)^n
=200/(1+4%)^1

2. Which would you prefer, \$200 today or \$200 in one year? Does your answer depend on when you need the money? Why or Why not?
We will prefer \$200 today due to the time value of money. This won't depend on the need of money as has got time value. We will prefer today as the amount can be reinvested to earn additional returns.

3.What is the no-arbitrage price of a security that pays cash flows of \$100 in one year and \$100 in two years?
\$189.00
\$519.00
...

#### Solution Summary

Response guides by providing steps to compute present value and arbitrage opportunity

\$2.49