Finance 314 Midterm 2 Study Guide

A car dealership offers a car for $14,000, with up to one year to pay for the car. If the interest rate is 5%, what is the net present value (NPV) of this offer to buyers who elect not to pay for the car for one year?

Basically, you are comparing the present value of the cost (-$14,000 in one year) to the benefit today (a $14,000 car). It is asking what amount of money you need to put in the bank today to have $14,000 in one year with an interest rate of 5%. Equation: NPV= PV(benefits) - PV(costs) NPV= 14,000 - (14,000/ (1+ .05) NPV= 14,000 - 13,333.33 Answer: The NPV of this offer is $667.

Consider a zero-coupon bond with a $1000 face value and 10 years left until maturity. If the YTM of this bond is 10.2%, then the price of this bond is closest to _______?

Explanation: A zero-coupon bond means that when you buy a bond, you won't receive multiple payments to get your face value back, you will get it all back at one time. In this question, you buy a bond today, and in 10 years, you will receive $1000 back, so you are trying to find the price of the bond you will buy today. Yield to maturity is like the interest rate, it is the return you will earn as an investor by buying the bond at its current market price, holding the bond to maturity, and receiving the promised face value payment. Equation: 1 + YTM = ((face value)/(price))^(1/n) or on a calculator: N: 10 I/Y: 10.2 PV: ? PMT:0 FV: 1000 Answer: $379 is the price of this bond.

Owen Inc. is expected to pay a $0.80 dividend at the end of the coming year. It is expected to sell for $16.00 at the end of the year. If Owen's equity cost of capital is 12%, what is its current stock price?

Explanation: Basically, the question asks what is the price you are going to pay today for a stock that at the end of the year, you can sell for $16 and receive a $.80 dividend? The rE, or equity cost of capital is 12%, meaning you'll make a 12% profit on whatever the price of the stock currently is. Equation: P0= (Div1 +P1)/ (1 + rE) P0= (.80 + 16)/ (1 + .12) Answer= $15 is the current stock price

A stock is bought for $23.00 and sold for $27.00 one year later, immediately after it has paid a dividend of $1.50. What is the capital gain rate for this transaction?

Explanation: The capital gain rate is the percent profit that you make from a stock after you sell it. Equation: Capital gain rate = (P1 - P0)/ P0 (27-23)/23 = .1739 Answer: The capital gain rate is 17.39%.

If the current inflation rate is 3.6% and you have an investment opportunity that pays 10.9%, then the real rate of interest on your investment is closest to ____?

Explanation: The investment opportunity (10.9%) is your nominal interest rate. The nominal interest rate does not take into account inflation rate, so you must find the real rate of interest to see exactly what % you will receive from your investment. Equation: (1 + nominal interest rate) = (1 + inflation rate)( 1 + real rate) you can manipulate this equation to: (real rate of interest) = ((1 + nominal rate)/(1 + inflation rate))- 1 ((1.109)/(1.036))-1 = 7.05% Answer: real rate of interest on your investment is closest to 7%

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 5 years. The bond certificate indicates that the stated coupon rate for this bond is 8.1% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 10.6%, then this bond will trade at ________.

Explanation: When asking if a bond will trade at discount, premium, or par, if the YTM and coupon rate is given, you don't need to do any calculations. Discount: YTM> coupon rate Premium: YTM< coupon rate Par: YTM = coupon rate Answer: This bond will trade at discount because YTM (10.6%) is greater than the coupon rate (8.1%)

What is the coupon payment of a 15-year $10,000 bond with a 9% coupon rate with semiannual payments?

Explanation: When you buy a bond, you are lending an organization money with the expectation that you will get it back (aka it is an investment). A 15-year $10,000 bond means you gave an organization $10,000 (the face value- FV) and expect to get it back in 15 years. A 9% coupon rate with semi annual payments means that every 6 months (semi annual), you will receive payments with 9% interest added to it. Equation: (FV * coupon rate)/ # of coupon payments (10,000 * .09)/ 2 = $450 Answer: $450 is the CPN, the amount you receive every 6 months for 15 years.

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 10 years. The bond certificate indicates that the stated coupon rate for this bond is 8.0% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 11.1%, then the price that this bond trades for will be closest to ________.

Step 1: Calculate the coupon payments (PMT) for the bond. (FV * coupon rate) / # of coupon payments (1000 * .8)/ 2 = 40 Step 2: Calculate the price of the bond (PV). N: 20 (10 yrs * 2 bc semiannual) I/Y: 5.55 (11.2 / 2) PV:? PMT: 40 FV: 1000 Answer: The price that this bond trades for will be closest to $816.

The Sisyphean Company has a bond outstanding with a face value of $5000 that reaches maturity in 8 years. The bond certificate indicates that the stated coupon rate for this bond is 8.2% and that the coupon payments are to be made semiannually. Assuming that this bond trades for $4541.53, then the YTM for this bond is closest to ________.

Step 1: Calculate the coupon payments (PMT) for the bond. (FV * coupon rate)/ # of coupon payments (5000 * .082)/ 2 = 205 Step 2: Find YTM (which is I/Y) N: 16 (8 years * 2 bc semiannual) I/Y:? PV: -4541.53 PMT: 205 FV: 5000 I/Y= 4.94 * 2 (bc semiannual) Answer: YTM is 9.9%

A $5000 bond with a coupon rate of 5.7% paid semiannually has ten years to maturity and a yield to maturity of 6.4%. If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond?

Step 1: Calculate the the coupon payments (PMT) for the bond. (FV * coupon rate) / # of coupon payments (5000 * .057)/ 2 = 142.50. (the denominator is 2 because it is semiannual payments. If it was annual payments, it would be 1) Step 2: Calculate the present value of the original coupon. N: 20 (bc 10 years semiannual so 10*2) I/Y: 3.2 (because YTM is 6.4 but semiannual so 6.4/2) PV:? PMT: 142.50 FV: 5000 PV= 4744.39 Step 3: Calculate the present value of the bond if the yield to maturity decreases by .8% to 5.6%. N:20 I/Y: 2.8 (5.6/2) PV:? PMT: 142.50 FV: 5000 PV= 5037.89 Step 4: Find difference between PVs $5037.89 - $4744.39 = $293.50 Answer: The price of the bond will use by $293.50.

The Busby Corporation had a share price at the start of the year of $26.10, paid a dividend of $0.59 at the end of the year, and had a share price of $29.50 at the end of the year. Which of the following is closest to the rate of return of investments in companies with equal risk to The Busby Corporation for this period?

The question is looking for rE, the equity cost of capital because it is the expected rate of return when purchasing a share/ stock. Equation: P0= (Div1 + P1)/ (1 + rE) $26.10 = (.59 + 29.50) / (1 + rE) --> (rE)= (30.09)/(26.10) - 1 rE= .1529 Answer: The closest rate of return of investments in companies with equal risk to the Busby Corporation is 15%.

JRN Enterprises just announced that it plans to cut its dividend from $3.00 to $1.50 per share and use the extra funds to expand its operations. Prior to this announcement, JRN's dividends were expected to grow indefinitely at 4% per year and JRN's stock was trading at $25.50 per share. With the new expansion, JRN's dividends are expected to grow at 8% per year indefinitely. Assuming that JRN's risk is unchanged by the expansion, the value of a share of JRN after the announcement is closest to ________.

This question is looking for the value of the share after the dividend changes using the constant dividend growth model, but it doesn't give you rE, so you have to find the equity cost of capital first. The rE will be the same for both dividend values because it says "JRN's risk is unchanged by the expansion". Step 1: Find rE using values from the original dividend. P0= (Div1)/ (rE- g) rE= (Div1/ P0) + g rE= (3/25.50) + .04 rE= .1577 or 15.77% Step 2: Apply rE to find the new value of the share. P0= (Div1)/ (rE- g) P0= (1.50)/ (.1577 - .08) Answer: The value of the new share is $19.32.

NoGrowth Industries presently pays an annual dividend of $1.20 per share and it is expected that these dividend payments will continue indefinitely. If NoGrowth's equity cost of capital is 10%, then the value of a share of NoGrowth's stock is closest to ________.

When a question asks for you to give the value of a share but only gives you a dividend, the equity cost of capital, and the growth rate, use the constant dividend growth model. It is looking for P0. Equation: The constant dividend growth model is: P0= (Div1)/ (rE - g) P0= (1.20)/ (.10 - 0) --> growth is 0 because the payments continue indefinitely, so they don't grow. Answer: The value of the share is closest to $12.