You just secured your dream job in New York City. You are now thinking about the possibility of buying an apartment. After searching, you fall in love with a $1 million- dollar apartment on the Upper West Side. You decide to take what you are learning in real estate finance into action to evaluate the mortgage! The market yield curve (based on the U.S. Treasury curve on Jan. 21, 2015) is given below. 

year(t):                    1    2        3     4       5      6            7            8 

10 year spot rate: .17   .53   .87   1.15   1.4    1.54      1.66     1.76 

  

Note that it is very difficult to borrow at the Treasury rate, even if the borrower has little or no default risk. This is because T-bill and T-notes contain a liquidity premium (Treasury securities serve as excellent collateral for many financial Transactions). 

Credit crunch and subprime turmoil have made borrowing even more difficult. Sup- pose that you can borrow at 100 basis points above the Treasury rate for all maturities (even if you have a perfect credit rating and will not default). The 100 basis points capture the liquidity premium for Treasury securities. (1 basis point is 0.01%.) 

To refresh your knowledge of the yield curve, consider the situation for borrowers who want to receive 100 dollars today and pay (everything including both the interest and the principal) back in two years. 

For example, as a default-free borrower who borrows at 100 basis points above the Treasury rate, you need to pay in the amount of 100× (1 + 0.53% + 1.00%)2 That is, the rate (y(2) + 1.00%) gives you the annualized interest rate for borrowing two years consecutively starting from today. 

year(t).      1 2 3 4 5 6 7 8 9 10 

cashflows 1 1  1  1  1 1  1  1  1  1   (cash flows are 1 for every year)

(QUESTION) Draw the Treasury zero-coupon yield curve. Comment on the shape of the current yield curve. Adding the 100 basis point to the Treasury rate, how much does it cost you today if you were to buy a balloon payment in the amount of $100 in 5 years (assuming you do not default)? 

(QUESTION) What is the present value of the following 10-year annuity? (Again, assume that there is no default and the borrowing is at 100 basis points above the Treasury rate for all maturity dates.) That is, the lender will be paid for sure a stream of $1 for ten years starting from Year 1. Let X denote the value of this annuity. Use the definition of spot rates and basic DCF analysis.