Question

Niendorf Corporation's 5-year bonds yield 6.75%, and 5-year T-bonds yield 4.80%. The real risk-free rate is r* = 2.75%, the inflation premium for 5-year bonds is IP =1.65%, the default risk premium for Niendorf's bonds is DRP = 1.20% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP= (t - 1) ´ 0.1%, where t = number of years to maturity. What is the liquidity premium (LP) on Niendorf's bonds?

Answer 1

Five-year bonds yield = 6.75%

Five-years T-bonds yield = 4.80%

Real risk-free rate is (r^*) = 2.75%

Inflation premium for five-year bonds (IP) = 1.65%

Default-risk premium (DRP) = 1.20%

r = r^* + IP + DRP + LP + MRP

r^* = real risk-free rate = 2.75%

IP = premium for expected inflation = 1.65%

DRP = premium for potential default risk = 1.20%

LP is the premium for lack of liquidity (or) marketability

MRP is the premium to compensate for the risk inherent in bonds with long maturities.

MRP = (t-1) * 0.1%

t = Number of years to maturity

t = 5 years

MRP = (5-1) * 0.1%

MRP = 4 * 0.1%

MRP = 0.004 (or) 0.4%

r = 2.75% + 1.65% + 1.20% + LP + 0.004

6.75% = 2.75% + 1.65% + 1.20% + LP + 0.4%

6.75% = 5.6% + LP + 0.4%

6.75% = 6% + LP

6% + LP = 6.75%

LP = 6.75% - 6%

LP = 0.75%

Liquidity premium (LP) = 0.75%

Answer 2

r(m) = r(f) + IP + MRP for treasury bond.
=> 4.8 = 2.75 + 1.65 + MRP
=> MRP = 0.4%
MRP = (t-1)*0.1 = 0.4, so, t =5
MRP = 0.4% for all bonds with t=5

for Niendorf,
r(m) = r(f) + IP + DRP + MRP +LP
=> 6.75 = 2.75 + 1.65 + 1.20 + 0.4 + LP
=> LP = 0.75% (NASWER)

Answer 3

R = R* + IP + DRP + LP + MRP

R = 6.75%
R* = 2.75%
IP = 1.65%
DRP =1.2%
MRP = (5-1)*.1% = .4%

Solve for Liquidity Premium

6.76 = 2.75 + 1.65 + 1.2 +.4 + LP

LP = .76%