Here the script. And here the slides.

Attention: the slides in the video contain a small typo in the formula you can see at 6:48. The result is correct.
In the numerator, 0.0125 and 0.015 should be switched.
The pdf slides have already been corrected.

In the video lesson, in order to compute the PD of a counterparty, namely the reference entity of the CDS, we have considered the formula

CS 1−R, where CS is the CDS spread and R is the recovery rate.

In reality that formula can be used in general (with caution!), every time we have some sort of credit spread. It is sufficient to read CS as “credit spread” and not only as “CDS spread”.

A very common credit spread is the so-called bond yield spread, that is to say the difference between the yield of a bond and the risk-free rate on the market.
(For the sake of completeness: in general the yield spread can be computed for every couple of bonds, and sometimes, especially in mathematical finance, it can be corrected by some minor factor).

Let’s start from the risk-free rate.
The risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. Such an investment does not exist in reality (everything is risky, because risk 0 does not exist!), but it is often assumed in mathematical finance.
In everyday business life, we can approximate the risk-free rate with the interest rate paid by (zero-coupon) bonds issued by AAA governments, whose probability of default is extremely low (but not 0!). Typical examples are the German bund or the three-month U.S. Treasury bill. By the way…why don’t you read this?

In general, the yield of a bond is the implicit rate of return of the bond. It is defined as the discount rate that, if applied to all the cash flows generated by a bond, gives a bond price equal to its market price (that is their difference is 0). Market price is usually computed using the zero term structure, but we skip that part.
An example is the simplest way to understand this.

Imagine we have a 2-year bond with face value (also known as par value) equal to €100, which pays 5% per annum semiannually, that is a coupon of €2.5 every 6 months. The market price of the bond (what we pay today to buy the bond) is €98.97.
What is the yield of the bond?

The yield is the rate y which solves the following equation:

 2.5exp(-0.5y)+2.5exp(-1y)+2.5exp(-1.5y)+102.5exp(-2y)-98.97=0 

Notice that we discount all coupons at the right time instant (0.5 = 6 months, 1= 1 year, and so on). Also notice that at the end of year 2 we get the coupon and also the face value of the bond, that is 102.5

Solving the previous expression is rather simple in R. We can use the function uniroot (type ?uniroot for more details).
We first define the object we want to solve:

f=function(y) 2.5*exp(-0.5*y)+2.5*exp(-1*y)+2.5*exp(-1.5*y)+102.5*exp(-2*y)-98.97

And then we apply uniroot, telling that our y is between 0 and 1 (and that makes sense for an interest rate…).

uniroot(f,lower=0,upper=1)

What we get is more or less y=0.0548.

Now, assume that the risk-free rate is 3% (this is a completely fictitious and unrealistic value!).

What is the bond yield spread of our bond?
Simply 0.0548-0.03=0.0248, or 2.48%.

This value can then be used in the formula above for estimating the PD of our counterparty. It is just another type of CS.