# Bond Valuation

0 r 1 2 n

...

CF1 CF2 CFn

Value

PV =

CF1

(1+ r )

1

+

CF2

(1 + r )

2

+ ... +

CFn

(1+ r )

n

.

Prof. P. Yourougou

MBC 633 – Managerial Finance

Lect. 03 - 2

Various Interest Rate Measures

Coupon rate Coupon rate

periodic cash flow a bond issuer contractually periodic cash flow a bond issuer contractually promises to pay a bond holder promises to pay a bond holder rates used by individual market participants to rates used by individual market participants to calculate fair present values (PV) calculate fair present values (PV) rates participants would earn by buying securities at rates participants would earn by buying securities at current market prices (P) current market prices (P) rates actually earned on investments rates actually earned on investments

Required rate of return (rrr) Required rate of return (rrr)

Expected rate of return (Err) Expected rate of return (Err) Realized rate of return (rr) Realized rate of return (rr)

Prof. P. Yourougou

MBC 633 – Managerial Finance

Lect. 03 - 3

Bond Valuation

Premium bond has Premium bond has

A coupon rate (INT) greater than the required A coupon rate (INT) greater than the required rate of return (rrr) and rate of return (rrr) and the fair present value of the bond (Vbb) is the fair present value of the bond (V ) is greater than the face value (M) greater than the face value (M)

Discount bond: if INT < rrr, then Vbb< M Discount bond: if INT < rrr, then V < M Par bond: if INT = rrr, then Vbb= M Par bond: if INT = rrr, then V = M

Prof. P. Yourougou

MBC 633 – Managerial Finance

Lect. 03 - 4

Required Rate of Return

The fair present value (PV) of a security is The fair present value (PV) of a security is determined using the required rate of return (rrr) as determined using the required rate of return (rrr) as the discount rate the discount rate

~ ~ ~ ~ CF3 CFn CF1 CF2 PV = + + + ... + (1 + rrr)1 (1 + rrr)2 (1 + rrr)3 (1 + rrr)n CF1 = cash flow in period tt(t = 1, …, n) CF1 = cash flow in period (t = 1, …, n) ~ = indicates the projected cash flow is uncertain ~ = indicates the projected cash flow is uncertain n = number of periods in the investment horizon n = number of periods in the investment horizon

Prof. P. Yourougou

MBC 633 – Managerial Finance

Lect. 03 - 5

Expected Rate of Return

The current market price (P) of a security is The current market price (P) of a security is determined using the expected rate of return (Err) determined using the expected rate of return (Err) as the discount rate as the discount rate

~ ~ ~ ~ CF3 CFn CF1 CF2 P= + + + ... + (1 + Err)n (1 + Err)1 (1 + Err)2 (1 + Err)3 CF1 = cash flow in period tt(t = 1, …, n) CF1 = cash flow in period (t = 1, …, n) ~ = indicates the projected cash flow is uncertain ~ = indicates the projected cash flow is uncertain n = number of periods in the investment horizon n = number of periods in the investment horizon

Prof. P. Yourougou

MBC 633 – Managerial Finance

Lect. 03 - 6

Realized Rate of Return

The realized rate of return (rr) is the discount rate that The realized rate of return (rr) is the discount rate that just equates the actual purchase price (( P) to the just equates the actual purchase price P) to the present value of the realized cash flows (RCFt)) tt(t = 1, present value of the realized cash flows (RCFt (t = 1, …, n) P …, n)

P=

RCF RCF RCF RCF 3 n 1 2 + + + ... + 1 2 3 (1 + rr) (1 + rr) (1 + rr) (1+ rr)n

Prof. P. Yourougou

MBC 633 – Managerial Finance

Lect. 03 - 7

Bond Valuation

The present value of a bond (Vb))can be written as: The present value of a bond (Vb can be written as:

⎞ INT 2T ⎛ M 1 Vb = ∑⎜ ⎜ (1 + i / 2) ⎟ + (1 + i / 2)2T ⎟ 2 t =1 ⎝ ⎠ d d = INT (PVIFA / 2, 2T ) + M (PFIV / 2, 2T ) i i 2 d d

t

M = the par value of the bond M = the par value of the bond INT = the annual interest (or coupon) payment INT = the annual interest...

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