An analyst evaluating securities has obtained the following information. The rea

Question

An analyst evaluating securities has obtained the following information. The real rate of interest is 2.9% and is expected to remain constant for the next 5 years. Inflation is expected to be 2.8% next year, 3.8% the following year, 4.8% the third year, and 5.8% every year thereafter. The maturity risk premium is estimated to be 0.1 × (t – 1)%, where t = number of years to maturity. The liquidity premium on relevant 5-year securities is 0.5% and the default risk premium on relevant 5-year securities is 1%.

a. What is the yield on a 1-year T-bill? Round your intermediate calculations and final answer to two decimal places.

%

b. What is the yield on a 5-year T-bond? Round your intermediate calculations and final answer to two decimal places.

%

c. What is the yield on a 5-year corporate bond? Round your intermediate calculations and final answer to two decimal places.

%

Explanation / Answer

The formula for calculating Yield on Treasury Bills is:

Yield on Treasury Bills (r) = r* + IP where r* = real risk free rate, IP = Inflation Premium

The formula for calculating Yield on Treasury Bonds is:

Yield on Treasury Securities (r) = r* + IP + MRP where r* = real risk free rate, IP = Inflation Premium and MRP = Market Risk Premium

The formula for calculating Yield on Corporate Bond is:

Yield on Corporate Bond (r) = r* + IP + MRP + DRP + LP where r* = real risk free rate, IP = Inflation Premium and MRP = Market Risk Premium, DRP = Default Risk Premium and LP = Liquidity Premium

__________________

a)

Here, r* = 2.9% and IP = 2.8%

Using these values in the above formula, we get,

Yield on on a 1-year T-bill (r1) = 2.9% + 2.8% = 5.70% (answer)

_________

b)

Here, r* = 2.9%, IP = (2.8% + 3.8% + 4.8% + 5.8% + 5.8%)/5 = 4.60% and MRP = .1*(5-1)% = .4%

Using these values in the above formula, we get,

Yield on on a 5-year T-Bond (r5) = 2.9% + 4.60% + .4% = 7.90% (answer)

_________

c)

Here, r* = 2.9%, IP = (2.8% + 3.8% + 4.8% + 5.8% + 5.8%)/5 = 4.60%, MRP = .1*(5-1)% = .4%, DRP = 1% and LP = .5%

Using these values in the formula for Yield on Corporate Bond, we get,

Yield on Corporate Bond (r5) = 2.9% + 4.60% + .4% + 1% + .5% = 9.4% (answer)

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