# Presentation: 195620

## TVM Applications

- TI BAII Plus

- Presentation

## Bond Valuation Model

*Bond Valuation is an application of Present Value.*
*The Value of the bond is the present value of all the cash flows the investor receives as a result of holding the bond.*
*3 Cash Flows*
- Amount that is paid to purchase the bond (PV)
- Periodic Interest Payments made to the bondholders (PMT)
- Repayment of Par value at end of Bond’s life.
*Other Terminology*
- Time frame for cash flows (N) = Bond’s Maturity
-  Interest Rate for Time Value is the rate at which future cash flows are being discounted to present.

## Bond Valuation Model

**IBM Bond Timeline:**

- 		Cur			Net
-     Bonds	Yld	Vol	Close	Chg
- AMR	61⁄424	cv	6	911⁄4	-11⁄2
- ATT	8.35s25	8.3	110	1023⁄4	+1⁄4
- IBM 6**3****/****8 **08	6.6	228	96**5****/****8 **	-**1****/****8 **
- Kroger 9s07	8.8	74	101**7****/****8 ****	****-**1⁄4

- Source: *Wall Street Journal*

- Investor that purchases bond today (2003) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.

## Bond Valuation Model

**IBM Bond Timeline:**

- Source: *Wall Street Journal*

- 63.75

- 63.75

- 63.75

- 63.75

- 63.75
- 1000.00

- Investor that purchases bond today (2003) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.

- 		Cur			Net
-     Bonds	Yld	Vol	Close	Chg
- AMR	61⁄424	cv	6	911⁄4	-11⁄2
- ATT	8.35s25	8.3	110	1023⁄4	+1⁄4
- IBM 6**3****/****8 **08	6.6	228	96**5****/****8 **	-**1****/****8 **
- Kroger 9s07	8.8	74	101**7****/****8 ****	****-**1⁄4

- 		Cur			Net
-     Bonds	Yld	Vol	Close	Chg
- AMR	61⁄424	cv	6	911⁄4	-11⁄2
- ATT	8.35s25	8.3	110	1023⁄4	+1⁄4
- IBM 6**3****/****8 **08	6.6	228	96**5****/****8 **	-**1****/****8 **
- Kroger 9s07	8.8	74	101**7****/****8 ****	****-**1⁄4

## Bond Valuation Model

**Compute Bond’s Intrinsic Value**

- 63.75

- 63.75

- 63.75

- 63.75

- 63.75
- 1000.00

- Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.

## Bond Valuation Model

**Compute Bond’s Intrinsic Value**

- 63.75

- 63.75

- 63.75

- 63.75

- 63.75
- 1000.00

- $63.75 Annuity for 5 years

- $1000 Lump Sum in 5 years

## Bond Valuation Model

**Some Bonds Pay Interest Semi-Annually:**

- 45

- 45.00
- 1000.00

- 45

- 45

- 45

- 45

- 45

- 45

- Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.

- Since interest is received every 6 months, need to use
- semi-annual compounding

## Bond Valuation Model

**Some Bonds Pay Interest Semi-Annually:**

- 45

- 45.00
- 1000.00

- 45

- 45

- 45

- 45

- 45

- 45

- Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.

## Yield to Maturity

*Bondholder’s Expected Rate of Return.*
- If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned?

## Yield to Maturity

- 63.75

- 63.75

- 63.75

- 63.75

- 63.75
- 1000.00

*Bondholder’s Expected Rate of Return.*
- If an investor purchases bond at today’s price and hold it until maturity, what is the annual rate of return that is earned?

- -966.25

**IBM Corporate Bond:**

## Yield to Maturity

- 63.75

- 63.75

- 63.75

- 63.75

- 63.75
- 1000.00

- -966.25

**IBM Corporate Bond:**

**7.203%**

**N**

**I/YR**

**PV**

**PMT**

**FV**

- 5     ?  -966.25  63.75  1,000

## Yield to Maturity

- 63.75

- 63.75

- 63.75

- 63.75

- 63.75
- 1000.00

- -966.25

**IBM Corporate Bond:**

**N**

**I/YR**

**PV**

**PMT**

**FV**

- 5     ?  -966.25  63.75  1,000

- If YTM > Coupon Rate bond Sells at a *DISCOUNT*
- If YTM < Coupon Rate bond Sells at a *PREMIUM*

**7.203%**

## Subsidized Financing

*Slick Willy Car Sales is willing to give you the choice of either $2,000 cash back, or 4 year - 1% financing on a purchase of a $20,000 SUV STOMPER.*
*Without the special financing, you could probably secure a similar loan at 5.0%*
*Ignoring possible tax issues, should you take the $2,000 cash back or go with the subidized financing?*
*What is the market value of the subsidized financing?*

## Subsidized Financing

- Strategy:
- Compare Payments under the two different scenarios.

- Scenario 1
- Loan = $18,000
- Interest Rate = 5%
- PV = 18,000
- FV = 0
- N = 48
- I = 5/12%
- PMT = ?

- Scenario 2
- Loan = $20,000
- Interest Rate = 1%
- PV = 20,000
- FV = 0
- N = 48
- I = 1/12%
- PMT = ?

## Subsidized Financing

- Scenario 1
- PV = 18,000
- FV = 0
- N = 48
- I = 5/12%
- PMT = ?

- Scenario 2
- PV = 20,000
- FV = 0
- N = 48
- I = 1/12%
- PMT = ?

- Scenario 1 : PMT = $414.53
- Scenario 2 : PMT = $425.23

## Subsidized Financing

- What is the market value of the loan subsidy?
- Step 1:  Determine the actual payments that would be made without the subsidy at current market rates.
- PV = 20,000           FV = 0
- N = 48                    I = 5/12%
- PMT = ?

## Subsidized Financing

- Payment of  $425.23 versus $460.59 is a $35.36 savings per month

- What is the market value of the loan subsidy?
- Step 1:  Determine the actual payments that would be made without the subsidy at current market rates.
- PV = 20,000           FV = 0
- N = 48                    I = 5/12%
- PMT = ?
- PMT = $460.59
- Step 2: Now determine the market value of the payment savings.

## Subsidized Financing

- The low interest financing is only worth the present value equivalent of $1,535.44

- Step 3:  Determine the present value of saving $35.36 per month for 48 months.
- PMT = $35.36        FV = 0
- N = 48                    I = 5/12%
- PV = -1,535.44