Mba611: Cost of Capital

MBA611: Problemset #1

Fall 2015

Problem #1

AUS Bank, a community bank that operates in the AUS campus only, sold bonds to raise capital.  AUS bonds have a coupon rate of 8% and coupons are paid annually. The par value is $1,000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?

Solution: Using the calculator:

• N = 5; I/Y = 11; PMT = 80 (8% of 1000); FV = 1,000
• CPT PV = ?

Problem #2

AUD Bank, a community bank that operates in the AUD campus only, also sold bonds to raise capital.  AUD bonds have a coupon rate of 10% and coupons are paid annually. The par value is $1,000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?

Solution: Using the calculator:

• N = 5; I/Y = 11; PMT = 100 (10% of 1000); FV = 1,000
• CPT PV = ?

Problem #3

The UAE Central Bank raised interest rates by 1% following the recent credit tightening around the world. Compare the % price changes of AUS and AUD bonds due to the interest rate change.

Solution: Using the calculator:

AUS

• N = 5; I/Y = 12; PMT = 80; FV = 1,000; CPT PV = ?

AUD

• N = 5; I/Y = 12; PMT = 100; FV = 1,000; CPT PV = ?

% Change in AUS bonds =

% Change in AUD bonds=

Problem #4:  What did you learn?

Solution:  Among other things, main points are

1. Prices of bonds are sensitive to interest rate changes.
2. Bonds that pay lower coupon are more sensitive to interest rate changes.

Problem #5:  What is the yield curve?  

Problem #6

AUS, 10-year, 6% coupon, paid semi-annually, bond is trading for $970. What is the implied cost of debt?

Problem #7

Collect monthly stock prices data of any U.S. stock from Yahoo Finance for the last 10 years and calculate monthly returns of the stock. Visit Fama-French website to collect – excess market returns monthly data for the same period.  Now you’ve 2 time-series data. Using excel, calculate ‘beta’ of the stock by running a simple regression (OLS). Calculate 10 years of average returns of the stock and use the CAPM equation to find a ‘guesstimate’ of cost of equity of the firm you are investigating.

Problem #8

Your community (the place you live) realized that it needs a new bridge to connect the community to Dubai. The engineering department of your community came up with a proposal that has the following project particulars. Your goal as a finance manager is to work with a bank to get financing/float an asset (the bridge) backed bond offering. Assume the discount rate used for all calculations – 10%.

Year  0 – You spend $100 to build the bridge  that takes about a year to complete.

Year 1 – revenue (from toll -- like Salik in Dubai) of $50 –use 90% of cash flow (revenue) for bond  payments.

Year 2 – revenue $30 – use 80% of cash flow (revenue) for bond  payments.

Year 3 – revenue $20  – use 70% of cash flow (revenue) for bond  payments.

Year 4 – revenue $10 -- – use 60% of cash flow (revenue) for bond  payments.

Year 5 through 10 – revenue $10 -- use 50% of cash flow (revenue) for bond  payments.

After year 10 – you do not charge any toll – free for the community – that is the social responsibility.  

Now answer the following questions:

THE BOTTOM LINE: First, you find whether it is feasible to undertake the project by looking at the projected cash flows. Next, you find how the project could be funded (externally) by looking at the profits from the project. If the project cannot be fully funded externally (outside investors), how much fund do you need internally?