Midland Oil is a US-based oil drilling company that is publicly traded and has estimated a dollar cost of equity of 8% for itself

US Treasury Bond Rate = 3.5%

US Market Risk Premium = 8%

Cost of Equity of Midland Oil Corp. = 8%

Now, As per Capital Assets Pricing Model,

Cost of Equity for Midland Oil Corp.  = US Treasury Bond Rate + Beta of Stock * Market Risk Premium

8% = 3.5% + Beta of Stock * 8%

Beta of Stock = (8% - 3.5%) / 8% = 0.5625

Beta of the Midland Oil Corp. is 0.5625.

Now, since the beta used by midland oil corp. in its calculations is 0.5625 and we can fairly assume that this beta would be applicable for most oil companies. This might not be true if the debt equity i.e. capital structure among companies in the sector is very different. But since nothing is given, we can assume that it would be almost similar. Hence beta of midland oil corp. would be almost same as of ColOil.

Thus, Beta of Col Oil = 0.5625.

Now, since the Midland Corp. is operating in the USA i.e. developed market while ColOil is operating in Columbia, ColOil does have some country specific risk with it which in the case of USA is almost 0. These risks are because of following factors:

1. Political Instability

2. Economic Conditions i.e. Recession, Depression etc.

3. Country Soverign credit rating and probability of default

4. Govt. Regulations etc.

Thus, we need to find out the country risk premium for the Col Oil. Below are the calculations for that:

US$ denominated Columbian Govt. Bonds Yield = 5%

US Treasury Rate = 3.5%

Columbian Soverign Default Risk Premium = US$ denominated Columbian Govt. Bonds Yield - US Treasury Rate

Columbian Soverign Default Risk Premium = 5% - 3.5%

Columbian Soverign Default Risk Premium = 1.5%

This is because all other parameters like currency, durations of bonds are same except the gpvernment backing the bonds. This means that columbian government needs to pay a yield of 1.5% extra to investors to entice them to buy their bonds than US$ bonds. But this default is for investment in columbian soveriegn debt. But ColOil represent risk of Columbian Stock Investment. Thus, it needs to be adjusted.

Standard Deviation of Columbian Equities = 25%

Standard Deviation of Columbian Debt = 20%

Columbian Equity Risk Premium Spread = Columbain Soverign Default Spread * Standard Deviation of Columbian Equities / Standard Deviation of Columbian Debt

Columbian Equity Risk Premium Spread = 1.5% * 25% / 20% = 1.875%

Thus, columbian equity risk premium spread is 1.875%. This means that investor would demand 1.875% higher from Columbian Equity market than US Equity Market.

Columbian Total Equity Risk Premium = US Equity Risk Premium + Columbian Equity Risk Premium Spread

Columbian Total Equity Risk Premium = 8% + 1.875% = 9.875%

This is the risk premium which any investor would demand for investing in Columbian Equity Market.

Risk Free Rate of Columbian Peso = Columbian Govt. Peso Yield - Columbain Soverign Default Spread

Risk Free Rate of Columbian Peso = 7% - 1.5% = 5.5%

This is the true risk free rate of Columbian Peso.

Now,

Risk Free Rate of Peso = 5.5%

Risk Premium of Columbian Equity Market = 9.875%

Beta of ColOil = 0.5625

As per Capital Assets Pricing Model,

Cost of Equity of ColOil = Risk Free Rate + Beta of ColOil * Risk Premium

Cost of Equity of ColOil = 5.5% + 0.5625 * 9.875% = 11.05%

Thus, cost of equity for ColOil in Columbian Peso should be 11.05%.